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PROPER MORPHISM

  • Proper morphism
  • Term in algebraic geometry

    X → Y be a morphism of schemes. The composition of two proper morphisms is proper. Any base change of a proper morphism f: X → Y is proper. That is, if

    Proper morphism

    Proper_morphism

  • Proper map
  • Mathematical map between topological spaces

    is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. There are

    Proper map

    Proper_map

  • Stein factorization
  • a proper morphism. Then one can write f = g ∘ f ′ {\displaystyle f=g\circ f'} where g : S ′ → S {\displaystyle g\colon S'\to S} is a finite morphism and

    Stein factorization

    Stein_factorization

  • Base change theorems
  • Relate the direct image and the pull-back of sheaves

    } Proper base change theorems for quasi-coherent sheaves apply in the following situation: f : X → S {\displaystyle f:X\to S} is a proper morphism between

    Base change theorems

    Base_change_theorems

  • Quasi-finite morphism
  • Type of morphism in algebraic geometry

    unramified at x. Finite morphisms are quasi-finite. A quasi-finite proper morphism locally of finite presentation is finite. Indeed, a morphism is finite if and

    Quasi-finite morphism

    Quasi-finite_morphism

  • Chow's lemma
  • algebraic geometry. It roughly says that a proper morphism is fairly close to being a projective morphism. More precisely, a version of it states the

    Chow's lemma

    Chow's_lemma

  • Glossary of algebraic geometry
  • a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism. Contents:  !$@ A B C D E F G H I J K L M N O P Q R S T U V W XYZ

    Glossary of algebraic geometry

    Glossary_of_algebraic_geometry

  • Morphism of schemes
  • Concept in algebraic geometry

    morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism

    Morphism of schemes

    Morphism_of_schemes

  • Coherent duality
  • Generalisations of Serre duality in mathematics

    of Jean-Pierre Serre was extended to a proper morphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or

    Coherent duality

    Coherent_duality

  • Proper
  • Topics referred to by the same term

    compact subsets are compact Proper morphism, in algebraic geometry, an analogue of a proper map for algebraic varieties Proper transfer function, a transfer

    Proper

    Proper

  • Complete variety
  • Type of algebraic variety

    of positive dimension is not complete. The morphism taking a complete variety to a point is a proper morphism, in the sense of scheme theory. An intuitive

    Complete variety

    Complete_variety

  • Finite morphism
  • Concept in algebraic geometry

    finite surjective morphism f: X → Y, X and Y have the same dimension. By Deligne, a morphism of schemes is finite if and only if it is proper and quasi-finite

    Finite morphism

    Finite_morphism

  • Nagata's compactification theorem
  • separated and finite type morphism to a Noetherian scheme S can be factored into an open immersion followed by a proper morphism. Nagata's original proof

    Nagata's compactification theorem

    Nagata's_compactification_theorem

  • Semi-continuity
  • Property of functions which is weaker than continuity

    morphism of schemes of finite presentation, then n X / Y {\displaystyle n_{X/Y}} is lower semicontinuous. If f {\displaystyle f} is a proper morphism

    Semi-continuity

    Semi-continuity

    Semi-continuity

  • Alexander Grothendieck
  • French mathematician (1928–2014)

    Projective tensor product Proper morphism – Term in algebraic geometry Pursuing Stacks – Seminal math text Quasi-finite morphism Quot scheme Ramanujam–Samuel

    Alexander Grothendieck

    Alexander Grothendieck

    Alexander_Grothendieck

  • Free monoid
  • Concept in mathematics

    respectively. The morphism f is determined by its values on the letters of B and conversely any map from B to M extends to a morphism. A morphism is non-erasing

    Free monoid

    Free_monoid

  • Decomposition theorem of Beilinson, Bernstein and Deligne
  • H^{l+m}(X;\mathbb {Q} )} Let f : X → Y {\displaystyle f:X\to Y} be a proper morphism between complex algebraic varieties such that X {\displaystyle X} is

    Decomposition theorem of Beilinson, Bernstein and Deligne

    Decomposition_theorem_of_Beilinson,_Bernstein_and_Deligne

  • Flat morphism
  • Scheme theory concept

    mathematics, in particular in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat

    Flat morphism

    Flat_morphism

  • Coherent sheaf cohomology
  • Concept in algebraic geometry

    a proper morphism were proved by Grothendieck (for locally Noetherian schemes) and by Grauert (for complex analytic spaces). Namely, for a proper morphism

    Coherent sheaf cohomology

    Coherent_sheaf_cohomology

  • Morph the Cat
  • 2006 studio album by Donald Fagen

    Morph the Cat is the third studio album by American singer-songwriter Donald Fagen. Released on March 7, 2006, to generally positive reviews from critics

    Morph the Cat

    Morph_the_Cat

  • Ample line bundle
  • Concept in algebraic geometry

    morphism has the property that L {\displaystyle L} is the pullback f ∗ O ( 1 ) {\displaystyle f^{*}{\mathcal {O}}(1)} . Conversely, for any morphism f

    Ample line bundle

    Ample_line_bundle

  • Arakelov theory
  • Mathematical theory

    of sheaves, and states that ch(f*(E))= f*(ch(E)TdX/Y), where f is a proper morphism from X to Y and E is a vector bundle over f. The arithmetic Riemann–Roch

    Arakelov theory

    Arakelov_theory

  • Scheme (mathematics)
  • Generalization of algebraic variety

    and the Hom functor on modules. Flat morphism, Smooth morphism, Proper morphism, Finite morphism, Étale morphism Stable curve Birational geometry Étale

    Scheme (mathematics)

    Scheme_(mathematics)

  • Grothendieck–Riemann–Roch theorem
  • Result in algebraic geometry

    . {\displaystyle H^{2\dim(X)-2d}(X,\mathbb {Q} ).} Now consider a proper morphism f : X → Y {\displaystyle f\colon X\to Y} between smooth quasi-projective

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch_theorem

  • Glossary of mathematical jargon
  • is different from n. This overloaded word is also non-jargon for a proper morphism. property A characteristic that a mathematical object may have or not;

    Glossary of mathematical jargon

    Glossary_of_mathematical_jargon

  • Finiteness theorem
  • Topics referred to by the same term

    finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical logic This disambiguation page

    Finiteness theorem

    Finiteness_theorem

  • Mongolia
  • Country in East Asia

    contiguous land empire in history. His grandson Kublai Khan conquered China proper and established the Yuan dynasty. After the collapse of the Yuan, the Mongols

    Mongolia

    Mongolia

    Mongolia

  • Étale cohomology
  • Sheaf cohomology on the étale site

    sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S (with f = gj), and as before the definition does not depend

    Étale cohomology

    Étale_cohomology

  • H topology
  • {\displaystyle \{X'\to X,Z\to X\}} where X ′ → X {\displaystyle X'\to X} is a proper morphism of finite presentation, Z → X {\displaystyle Z\to X} is a closed immersion

    H topology

    H_topology

  • Polymorphism (biology)
  • Species having two or more distinct forms

    for classical genetics by John Maynard Smith (1998). The shorter term morphism was preferred by the evolutionary biologist Julian Huxley (1955). Various

    Polymorphism (biology)

    Polymorphism (biology)

    Polymorphism_(biology)

  • Chow group
  • Analogs of homology groups for algebraic varieties

    associated to the proper morphism Z → X {\displaystyle Z\to X} , and the second homomorphism is pullback with respect to the flat morphism X − Z → X {\displaystyle

    Chow group

    Chow_group

  • Resolution of singularities
  • Concept in algebraic geometry

    regular variety W. A strong desingularization of X is given by a proper birational morphism from a regular variety W′ to W subject to some of the following

    Resolution of singularities

    Resolution of singularities

    Resolution_of_singularities

  • Fiber product of schemes
  • Construction in algebraic geometry

    {Spec} (A\otimes _{B}C).} The morphism X ×Y Z → Z is called the base change or pullback of the morphism X → Y via the morphism Z → Y. In some cases, the fiber

    Fiber product of schemes

    Fiber_product_of_schemes

  • Category (mathematics)
  • Mathematical object that generalizes the standard notions of sets and functions

    a morphism 1 x : x → x {\displaystyle 1_{x}:x\to x} (some authors write id x {\displaystyle \operatorname {id} _{x}} ) called the identity morphism for

    Category (mathematics)

    Category (mathematics)

    Category_(mathematics)

  • Elliptic surface
  • Mathematical concept

    surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers

    Elliptic surface

    Elliptic_surface

  • Valuative criterion
  • A and X' denotes the generic point of Y' , then for every morphism Y' → Y and every morphism X' → X which lifts the generic point, then there exists at

    Valuative criterion

    Valuative_criterion

  • Sheaf (mathematics)
  • Tool to track locally defined data attached to the open sets of a topological space

    X {\displaystyle X} . A morphism φ : F → G {\displaystyle \varphi :{\mathcal {F}}\to {\mathcal {G}}} consists of a morphism φ U : F ( U ) → G ( U ) {\displaystyle

    Sheaf (mathematics)

    Sheaf_(mathematics)

  • Group action
  • Transformations induced by a mathematical group

    G-maps. The composition of two morphisms is again a morphism. If a morphism f is bijective, then its inverse is also a morphism. In this case f is called an

    Group action

    Group action

    Group_action

  • Algebraic space
  • Generalization of a scheme

    such that There is a surjective étale morphism h X → X {\displaystyle h_{X}\to {\mathfrak {X}}} the diagonal morphism Δ X / S : X → X × X {\displaystyle

    Algebraic space

    Algebraic_space

  • Coherent sheaf
  • Generalization of vector bundles

    sections. Let f : X → Y {\displaystyle f:X\to Y} be a morphism of ringed spaces (for example, a morphism of schemes). If F {\displaystyle {\mathcal {F}}} is

    Coherent sheaf

    Coherent_sheaf

  • Algebraic K-theory
  • Subject area in mathematics

    Chern character and Todd class of X. Additionally, he proved that a proper morphism f : X → Y to a smooth variety Y determines a homomorphism f* : K(X)

    Algebraic K-theory

    Algebraic_K-theory

  • Adjoint functors
  • Relationship between two functors abstracting many common constructions

    every C-morphism f : FY → X, there is a unique D-morphism ΦY, X(f) = g : Y → GX, and for every D-morphism g : Y → GX, there is a unique C-morphism Φ−1Y,

    Adjoint functors

    Adjoint_functors

  • Endomorphism
  • Self-self morphism

    object to itself. More generally in category theory, an endomorphism is a morphism from an object in some category to itself. An endomorphism that is also

    Endomorphism

    Endomorphism

    Endomorphism

  • Riemann–Roch-type theorem
  • Theorem in geometry

    {\displaystyle A_{*}(X)} is the rational Chow group of X, for each proper morphism f, G ∗ ( f ) , A ∗ ( f ) {\displaystyle G_{*}(f),A_{*}(f)} are the

    Riemann–Roch-type theorem

    Riemann–Roch-type_theorem

  • Dévissage
  • Mathematical technique in algebraic geometry

    restriction of f to X′ such that X′ → T is a finite morphism and T → S is a smooth affine morphism with geometrically integral fibers of dimension n. Denote

    Dévissage

    Dévissage

  • Theorem on formal functions
  • states the following: Let f : X → S {\displaystyle f:X\to S} be a proper morphism of noetherian schemes with a coherent sheaf F {\displaystyle {\mathcal

    Theorem on formal functions

    Theorem_on_formal_functions

  • Initial and terminal objects
  • Special objects used in (mathematical) category theory

    a universal morphism from • to U. The functor which sends • to I is left adjoint to U. A terminal object T in C is a universal morphism from U to •.

    Initial and terminal objects

    Initial_and_terminal_objects

  • Class (set theory)
  • Collection of sets in mathematics that can be defined based on a property of its members

    objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category. The surreal numbers are a proper class of objects

    Class (set theory)

    Class_(set_theory)

  • Local invariant cycle theorem
  • Invariant cycle theorem

    the BBD decomposition. Deligne also proved the following. Given a proper morphism X → S {\displaystyle X\to S} over the spectrum S {\displaystyle S}

    Local invariant cycle theorem

    Local_invariant_cycle_theorem

  • Zariski's main theorem
  • Theorem of algebraic geometry and commutative algebra

    point under a proper birational morphism is connected. A generalization due to Grothendieck describes the structure of quasi-finite morphisms of schemes

    Zariski's main theorem

    Zariski's_main_theorem

  • Morph (X-Men: The Animated Series)
  • Fictional character

    known; Morph continues to use he/him pronouns within the series. Despite this announcement, Rogue does at one point refer to Morph using the proper pronouns

    Morph (X-Men: The Animated Series)

    Morph_(X-Men:_The_Animated_Series)

  • Zariski's connectedness theorem
  • conditions the fibers of a morphism of varieties are connected. It is an extension of Zariski's main theorem to the case when the morphism of varieties need not

    Zariski's connectedness theorem

    Zariski's_connectedness_theorem

  • Yoneda lemma
  • Embedding of categories into functor categories

    {\mathcal {C}}} ) to the morphism f ∘ − {\displaystyle f\circ -} (composition with f {\displaystyle f} on the left) that sends a morphism g {\displaystyle g}

    Yoneda lemma

    Yoneda_lemma

  • Isomorphism
  • In mathematics, invertible homomorphism

    In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse

    Isomorphism

    Isomorphism

    Isomorphism

  • List of algebraic geometry topics
  • algébrique Fiber product of schemes Flat morphism Smooth scheme Finite morphism Quasi-finite morphism Proper morphism Semistable elliptic curve Grothendieck's

    List of algebraic geometry topics

    List_of_algebraic_geometry_topics

  • Exact sequence
  • Sequence of homomorphisms such that each kernel equals the preceding image

    morphism t : B → A {\displaystyle t:B\to A} such that t ∘ f {\displaystyle t\circ f} is the identity on A {\displaystyle A} . There exists a morphism

    Exact sequence

    Exact sequence

    Exact_sequence

  • Coproduct
  • Category-theoretic construction

    then we have a unique morphism X → Z {\displaystyle X\rightarrow Z} (since Z {\displaystyle Z} is terminal) and thus a morphism X ⊕ Y → Z ⊕ Y {\displaystyle

    Coproduct

    Coproduct

  • Hom functor
  • Functor mapping hom objects to an underlying category

    observes that every morphism h : A′ → A gives rise to a natural transformation Hom(h, –) : Hom(A, –) → Hom(A′, –) and every morphism f : B → B′ gives rise

    Hom functor

    Hom_functor

  • Projective variety
  • Algebraic variety in a projective space

    is a finite morphism. Projections can be used to cut down the dimension in which a projective variety is embedded, up to finite morphisms. Start with

    Projective variety

    Projective variety

    Projective_variety

  • Embedding
  • Inclusion of one mathematical structure in another, preserving properties of interest

    {\displaystyle f} is a morphism f g : C → B {\displaystyle fg:C\rightarrow B} , then g {\displaystyle g} itself is a morphism. A factorization system

    Embedding

    Embedding

  • Differential graded category
  • Concept in homological algebra

    category, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with the additional structure of a differential graded

    Differential graded category

    Differential_graded_category

  • Six operations
  • Formalism in homological algebra

    product is left adjoint to internal Hom. Let f : X → Y be a morphism of schemes. The morphism f induces several functors. Specifically, it gives adjoint

    Six operations

    Six_operations

  • Moduli stack of elliptic curves
  • Algebraic stack in mathematics

    scheme as elliptic curves have non-trivial automorphisms. There is a proper morphism of M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} to the affine line

    Moduli stack of elliptic curves

    Moduli_stack_of_elliptic_curves

  • Lift (mathematics)
  • a branch of mathematics, given a morphism f: X → Y and a morphism g: Z → Y, a lift or lifting of f to Z is a morphism h: X → Z such that f = g ∘ h (in

    Lift (mathematics)

    Lift_(mathematics)

  • Stack (mathematics)
  • Generalisation of a sheaf; a fibered category that admits effective descent

    {\displaystyle y} by F {\displaystyle F} . This means a morphism with image F {\displaystyle F} such that any morphism g : z → y {\displaystyle g:z\to y} with image

    Stack (mathematics)

    Stack_(mathematics)

  • Abelian variety
  • Projective variety that is also an algebraic group

    abelian varieties carry the structure of a group. A morphism of abelian varieties is a morphism of the underlying algebraic varieties that preserves

    Abelian variety

    Abelian variety

    Abelian_variety

  • Lie groupoid
  • Internal groupoid in the category of smooth manifolds

    morphism between two Lie groupoids G ⇉ M {\displaystyle G\rightrightarrows M} and H ⇉ N {\displaystyle H\rightrightarrows N} is a groupoid morphism F

    Lie groupoid

    Lie_groupoid

  • Direct image functor
  • In mathematics, a mapping between categories

    sheaf or pushforward sheaf of F along f. Since a morphism of sheaves φ: F → G on X gives rise to a morphism of sheaves f∗(φ): f∗(F) → f∗(G) on Y in an obvious

    Direct image functor

    Direct_image_functor

  • Hilbert scheme
  • Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor

    natural morphism to an n-th symmetric product of M. This morphism is birational for M of dimension at most 2. For M of dimension at least 3 the morphism is

    Hilbert scheme

    Hilbert_scheme

  • Kripke semantics
  • Formal semantics for non-classical logic systems

    Kripke semantics are called p-morphisms (which is short for pseudo-epimorphism, but the latter term is rarely used). A p-morphism of Kripke frames ⟨ W , R

    Kripke semantics

    Kripke_semantics

  • Proper model structure
  • Special kind of model structure

    which all objects are fibrant, is right proper. For a model category M {\displaystyle {\mathcal {M}}} and a morphism f : X → Y {\displaystyle f\colon X\rightarrow

    Proper model structure

    Proper_model_structure

  • Normal scheme
  • Concept in algebraic geometry

    finite birational morphism from any variety Y to X is an isomorphism.[citation needed] Normal varieties were introduced by Zariski. A morphism of varieties

    Normal scheme

    Normal_scheme

  • Segre class
  • contained in the following. Let p : X → Y {\displaystyle p:X\to Y} be a proper morphism between algebraic schemes such that Y {\displaystyle Y} is irreducible

    Segre class

    Segre_class

  • Fundamental group scheme
  • perfect and X → Spec ( k ) {\displaystyle X\to {\text{Spec}}(k)} is a proper morphism of schemes with X {\displaystyle X} reduced and connected scheme. Assuming

    Fundamental group scheme

    Fundamental_group_scheme

  • Rational function
  • Ratio of polynomial functions

    Q 1 ( x ) . {\displaystyle \textstyle {\frac {P_{1}(x)}{Q_{1}(x)}}.} A proper rational function is a rational function in which the degree of P ( x )

    Rational function

    Rational_function

  • Allegory (mathematics)
  • category in which every morphism R : X → Y {\displaystyle R\colon X\to Y} is associated with an anti-involution, i.e. a morphism R ∘ : Y → X {\displaystyle

    Allegory (mathematics)

    Allegory_(mathematics)

  • Semistable reduction theorem
  • Mathematical theory in the field of algebraic geometry

    reduction theorems state that, given a proper flat morphism of schemes X → S {\displaystyle X\to S} , there exists a morphism S ′ → S {\displaystyle S'\to S}

    Semistable reduction theorem

    Semistable_reduction_theorem

  • Relative effective Cartier divisor
  • constructed as a fiber of a morphism; namely, viewing L as the total space of it, the section s is a X-morphism of L: a morphism s : X → L {\displaystyle

    Relative effective Cartier divisor

    Relative_effective_Cartier_divisor

  • Category of sets
  • Category whose objects are sets and whose morphisms are functions

    objects are sets. The arrows or morphisms between sets A and B are the functions from A to B, and the composition of morphisms is the composition of functions

    Category of sets

    Category_of_sets

  • Portmanteau
  • Word consisting of two words

    nɒt/ becoming /doʊnt/); however, don't is also an example of a portmanteau morph. A blend also differs from a compound, which fully preserves the stems of

    Portmanteau

    Portmanteau

    Portmanteau

  • Glossary of category theory
  • sends cartesian morphisms to cartesian morphisms. cartesian morphism 1.  Given a functor π: C → D (e.g., a prestack over schemes), a morphism f: x → y in

    Glossary of category theory

    Glossary_of_category_theory

  • Weil restriction
  • Restriction of scalars

    extension. Under appropriate hypotheses (e.g., flat, proper, finitely presented), any morphism T → S {\displaystyle T\to S} of algebraic spaces yields

    Weil restriction

    Weil_restriction

  • Affine variety
  • Algebraic variety defined within an affine space

    in the Zariski topology on An × Am , but not in the product topology. A morphism, or regular map, of affine varieties is a function between affine varieties

    Affine variety

    Affine variety

    Affine_variety

  • Localization of a category
  • in C, but the morphisms are enhanced by adding a formal inverse for each morphism in W. Under suitable hypotheses on W, the morphisms from an object

    Localization of a category

    Localization_of_a_category

  • Complete lattice
  • Partially ordered set in which all subsets have both a supremum and infimum

    meets if and only if it is an upper adjoint. As such, each join-preserving morphism determines a unique upper adjoint in the inverse direction that preserves

    Complete lattice

    Complete lattice

    Complete_lattice

  • Equivalence of categories
  • Abstract mathematics relationship

    c} and all morphisms to 1 c {\displaystyle 1_{c}} . By contrast, the category C {\displaystyle C} with a single object and a single morphism is not equivalent

    Equivalence of categories

    Equivalence_of_categories

  • Joyal model structure
  • Model structure on the category of simplicial sets

    initial morphism ∅ → ! X {\displaystyle \emptyset \xrightarrow {!} X} is a cofibration, are all simplicial sets. The Joyal model structure is left proper, which

    Joyal model structure

    Joyal_model_structure

  • Darcy Proper
  • American mastering engineer

    Darcy Proper is an American mastering engineer based in Auburn, NY. In 2008, she became the first woman engineer to win a Grammy for the Best Surround

    Darcy Proper

    Darcy_Proper

  • Category of rings
  • Category whose objects are rings and whose morphisms are ring homomorphisms

    morphism is a monomorphism. This follows from the fact that the only ideals in a field F are the zero ideal and F itself. One can then view morphisms

    Category of rings

    Category_of_rings

  • Filter (mathematics)
  • Special subset of a partially ordered set

    P, then F is said to be a proper filter. Authors in set theory and mathematical logic often require all filters to be proper; this article will eschew

    Filter (mathematics)

    Filter (mathematics)

    Filter_(mathematics)

  • Deterministic context-free language
  • Subset of languages in formal theory

    following operations: union intersection concatenation Kleene star ε-free morphism Mirror image The languages of this class have great practical importance

    Deterministic context-free language

    Deterministic_context-free_language

  • Simplicial set
  • Mathematical construction used in homotopy theory

    single morphism from i to j whenever i ≤ j. Concretely, the n-simplices of the nerve NC can be thought of as sequences of n composable morphisms in C:

    Simplicial set

    Simplicial_set

  • Séminaire Nicolas Bourbaki (1950–1959)
  • Chevalley, La notion de correspondance propre en géométrie algébrique (proper morphisms) Marcel Guillaume, Les tableaux sémantiques du calcul des prédicats

    Séminaire Nicolas Bourbaki (1950–1959)

    Séminaire_Nicolas_Bourbaki_(1950–1959)

  • Podarcis muralis
  • Common wall lizard

    these morphs. For example, in orange morphs, sexual selection favours larger morphs which makes them, on average, larger than the other morphs. The femoral

    Podarcis muralis

    Podarcis muralis

    Podarcis_muralis

  • Constructible set (topology)
  • of maps (or "morphisms"). The key result is: Chevalley's theorem. If f : X → Y {\displaystyle f:X\to Y} is a finitely presented morphism of schemes and

    Constructible set (topology)

    Constructible_set_(topology)

  • Derived category
  • Homological construction

    {\displaystyle f_{i+1}\circ d_{X}^{i}=d_{Y}^{i}\circ f_{i}} . Such a morphism induces morphisms on cohomology groups H i ( f ∙ ) : H i ( X ∙ ) → H i ( Y ∙ ) {\displaystyle

    Derived category

    Derived_category

  • Néron model
  • Mathematical model

    a smooth separated scheme over R then any K-morphism from XK to AK can be extended to a unique R-morphism from X to AR (Néron mapping property). In particular

    Néron model

    Néron_model

  • Dualizing sheaf
  • Concept from algebraic geometry

    the above duality holds for any locally free sheaf. Given a proper finitely presented morphism of schemes f : X → Y {\displaystyle f:X\to Y} , (Kleiman 1980)

    Dualizing sheaf

    Dualizing_sheaf

  • Graph homomorphism
  • Structure-preserving correspondence between node-link graphs

    with no homomorphism to any proper subgraph. Equivalently, a core can be defined as a graph that does not retract to any proper subgraph. Every graph G is

    Graph homomorphism

    Graph homomorphism

    Graph_homomorphism

  • Function composition
  • Operation on mathematical functions

    are axiomatized and generalized in category theory with the concept of morphism as the category-theoretical replacement of functions. The reversed order

    Function composition

    Function_composition

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PROPER MORPHISM

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PROPER MORPHISM

  • PROSPER
  • Male

    English

    PROSPER

    English name derived from Latin Prosperus, PROSPER means "fortunate, successful."

    PROSPER

  • Cromer
  • Surname or Lastname

    French

    Cromer

    French : from a Germanic personal name, Hrodmar, composed of hrōd ‘renown’, ‘glory’ + mār ‘famous’.English : habitational name from Cromer in Norfolk, recorded in the 13th century as Crowemere, from Old English crāwe ‘crow’ + mere ‘lake’.Variant spelling of German and Jewish Kromer.

    Cromer

  • FRODER
  • Male

    Norwegian

    FRODER

    Norwegian variant form of Scandinavian Frode, FRODER means "wise."

    FRODER

  • Prosper
  • Boy/Male

    Australian, Christian, Danish, Finnish, French, German, Latin

    Prosper

    Fortunate

    Prosper

  • PIPER
  • Male

    English

    PIPER

    English occupational surname transferred to unisex forename use, derived from Middle English pipere, PIPER means "pipe-player."

    PIPER

  • Prater
  • Surname or Lastname

    English

    Prater

    English : status name for a reeve, the chief magistrate or bailiff of a district, from Latin praetor.Dutch : occupational name for a warden of meadows or a gamekeeper, from Middle Dutch prater, preter (Latin pratarius, a derivative of pratum ‘meadow’).Dutch and North German : nickname for an excessively talkative person, from Middle Low German praten ‘to talk or prattle’.German : variant of Brater (see Brader 2).

    Prater

  • Piper
  • Girl/Female

    English American

    Piper

    Piper.

    Piper

  • Cooper
  • Surname or Lastname

    English

    Cooper

    English : occupational name for a maker and repairer of wooden vessels such as barrels, tubs, buckets, casks, and vats, from Middle English couper, cowper (apparently from Middle Dutch kūper, a derivative of kūp ‘tub’, ‘container’, which was borrowed independently into English as coop). The prevalence of the surname, its cognates, and equivalents bears witness to the fact that this was one of the chief specialist trades in the Middle Ages throughout Europe. In America, the English name has absorbed some cases of like-sounding cognates and words with similar meaning in other European languages, for example Dutch Kuiper.Jewish (Ashkenazic) : Americanized form of Kupfer and Kupper (see Kuper).Dutch : occupational name for a buyer or merchant, Middle Dutch coper.

    Cooper

  • Roper
  • Surname or Lastname

    English

    Roper

    English : occupational name for a maker or seller of rope, from an agent derivative of Old English rāp ‘rope’. See also Roop.Variant of French Robert.North German (Röper) : occupational name for a town crier, from an agent derivative of Middle Low German rōpen ‘to call’.

    Roper

  • Prospera
  • Girl/Female

    Latin

    Prospera

    Prosper.

    Prospera

  • Pepper
  • Surname or Lastname

    English and North German

    Pepper

    English and North German : from Middle English peper, piper, Middle Low German peper ‘pepper’, hence a metonymic occupational name for a spicer; alternatively, it may be a nickname for a small man (as if the size of a peppercorn) or one with a fiery temper, or for a dark-haired person (from the color of a peppercorn) or anecdotal for someone who paid a peppercorn rent.Americanized form of the Ashkenazic Jewish ornamental name Pfeffer, or Fef(f)er, a cognate, from Yiddish fefer ‘pepper’.Irish : variant of Peppard.

    Pepper

  • PROSPERO
  • Male

    Italian

    PROSPERO

    Italian and Spanish form of Latin Prosperus, PROSPERO means "fortunate, successful." Shakespeare used this name in his play "The Tempest."

    PROSPERO

  • Porter
  • Surname or Lastname

    English and Scottish

    Porter

    English and Scottish : occupational name for the gatekeeper of a walled town or city, or the doorkeeper of a great house, castle, or monastery, from Middle English porter ‘doorkeeper’, ‘gatekeeper’ (Old French portier). The office often came with accommodation, lands, and other privileges for the bearer, and in some cases was hereditary, especially in the case of a royal castle. As an American surname, this has absorbed cognates and equivalents in other European languages, for example German Pförtner (see Fortner) and North German Poertner.English : occupational name for a man who carried loads for a living, especially one who used his own muscle power rather than a beast of burden or a wheeled vehicle. This sense is from Old French porteo(u)r (Late Latin portator, from portare ‘to carry or convey’).Dutch : occupational name from Middle Dutch portere ‘doorkeeper’. Compare 1.Dutch : status name for a freeman (burgher) of a seaport, Middle Dutch portere, modern Dutch poorter.Jewish (Ashkenazic) : adoption of the English or Dutch name in place of some Ashkenazic name of similar sound or meaning.

    Porter

  • Pepper
  • Boy/Male

    British, Chinese, English

    Pepper

    From the Pepper Plant

    Pepper

  • PORTER
  • Male

    English

    PORTER

    English occupational surname transferred to forename use, PORTER means "doorkeeper."

    PORTER

  • Pepper
  • Girl/Female

    American, Australian, British, English

    Pepper

    From the Pepper Plant; Hot Spice

    Pepper

  • Draper
  • Surname or Lastname

    English and Irish

    Draper

    English and Irish : occupational name for a maker and seller of woolen cloth, Anglo-Norman French draper (Old French drapier, an agent derivative of drap ‘cloth’). The surname was introduced to Ulster in the 17th century. Draperstown in County Londonderry was named for the London Company of Drapers, which was allocated the land in the early 17th century.

    Draper

  • Roper
  • Boy/Male

    English

    Roper

    Maker of rope.

    Roper

  • Grover
  • Boy/Male

    English American

    Grover

    Grove dweller. Used as both surname and given name. Famous bearer: American president Grover...

    Grover

  • Piper
  • Girl/Female

    American, Australian, British, Chinese, English

    Piper

    Flute Player; A Young Dove; Piper

    Piper

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PROPER MORPHISM

  • Appropriately
  • adv.

    In an appropriate or proper manner; fitly; properly.

  • Improper
  • a.

    Not proper; not suitable; not fitted to the circumstances, design, or end; unfit; not becoming; incongruous; inappropriate; indecent; as, an improper medicine; improper thought, behavior, language, dress.

  • Proper
  • a.

    Rightly so called; strictly considered; as, Greece proper; the garden proper.

  • Proped
  • n.

    Same as Proleg.

  • Prefer
  • v. t.

    To carry or bring (something) forward, or before one; hence, to bring for consideration, acceptance, judgment, etc.; to offer; to present; to proffer; to address; -- said especially of a request, prayer, petition, claim, charge, etc.

  • Unproper
  • a.

    Not proper or peculiar; improper.

  • Grooper
  • n.

    See Grouper.

  • Primer
  • n.

    A kind of type, of which there are two species; one, called long primer, intermediate in size between bourgeois and small pica [see Long primer]; the other, called great primer, larger than pica.

  • Pepper
  • n.

    Any plant of the genus Capsicum, and its fruit; red pepper; as, the bell pepper.

  • Pauper
  • n.

    A poor person; especially, one development on private or public charity. Also used adjectively; as, pouper immigrants, pouper labor.

  • Pepper
  • v. t.

    To sprinkle or season with pepper.

  • Proper
  • a.

    Pertaining to one of a species, but not common to the whole; not appellative; -- opposed to common; as, a proper name; Dublin is the proper name of a city.

  • Cooper
  • n.

    Work done by a cooper in making or repairing barrels, casks, etc.; the business of a cooper.

  • Proper
  • adv.

    Properly; hence, to a great degree; very; as, proper good.

  • Hooper
  • n.

    One who hoops casks or tubs; a cooper.

  • Pamper
  • v. t.

    To gratify inordinately; to indulge to excess; as, to pamper pride; to pamper the imagination.

  • Cooper
  • v. t.

    To do the work of a cooper upon; as, to cooper a cask or barrel.

  • Proper
  • a.

    Befitting one's nature, qualities, etc.; suitable in all respect; appropriate; right; fit; decent; as, water is the proper element for fish; a proper dress.

  • Proper
  • a.

    Belonging to the natural or essential constitution; peculiar; not common; particular; as, every animal has his proper instincts and appetites.

  • Groper
  • n.

    One who gropes; one who feels his way in the dark, or searches by feeling.