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In mathematics, the Shimura subgroup Σ(N) is a subgroup of the Jacobian of the modular curve X0(N) of level N, given by the kernel of the natural map
Shimura_subgroup
Japanese mathematician (1930–2019)
Gorō Shimura (志村 五郎, Shimura Gorō; 23 February 1930 – 3 May 2019) was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics
Goro_Shimura
Mathematical concept
Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are not algebraic varieties but are
Shimura_variety
Cohomology theory
cusps c of a fundamental domain of G, and Gc is the subgroup fixing the cusp c. The Eichler–Shimura isomorphism is an isomorphism between the space of
Eichler–Shimura_isomorphism
groups over local fields, a hyperspecial subgroup of a reductive group G is a certain type of compact subgroup of G. In particular, let F be a nonarchimedean
Hyperspecial_subgroup
Complex multiplication field
Another name used is J-field. The abbreviation "CM" was introduced by Shimura and Taniyama. A number field K is a CM-field if it is a quadratic extension
CM-field
1995 publication in mathematics
also probably be used to disprove the Taniyama–Shimura–Weil conjecture. Therefore, if the Taniyama–Shimura–Weil conjecture were true, no set of numbers
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Matrix group
subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of
Congruence_subgroup
modular forms, a Maass–Shimura operator is an operator which maps modular forms to almost holomorphic modular forms. The Maass–Shimura operator on (almost
Maass–Shimura_operator
36 mathematical problems stated in 1955
Taniyama's twelfth and thirteenth problems were the precursor to the Taniyama–Shimura conjecture, also known as the modularity theorem, which would be used in
Taniyama's_problems
Type of group in group theory
algebraic subgroup of G L n ( Q ) {\displaystyle \mathrm {GL} _{n}(\mathbb {Q} )} for some n {\displaystyle n} then we can define an arithmetic subgroup of G
Arithmetic_group
convolution. It can also be defined for a pair (g, K) of a maximal compact subgroup K of a Lie group with Lie algebra g, in which case the Hecke algebra is
Hecke_algebra_of_a_pair
Mathematician
techniques, in which the arithmetic and geometry of modular curves and of Shimura varieties play a central role, and have strong links with the discoveries
Yunqing_Tang
Analytic function on the upper half-plane with a certain behavior under the modular group
has absolute value ≤ 2p11/2. This was confirmed by the work of Eichler, Shimura, Kuga, Ihara, and Pierre Deligne as a result of Deligne's proof of the
Modular_form
2002 single by Minimoni
Project subgroup Minimoni. It was released on April 24, 2002 and sold 212,230 copies. This single was a collaboration with comedian Ken Shimura in his
Aīn_Taisō_/_Aīn!_Dance_no_Uta
Mathematical conjecture
Richard Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André–Oort conjecture. In the case of
Zilber–Pink_conjecture
Branch of algebraic geometry
1995. In the 1960s, Goro Shimura introduced Shimura varieties as generalizations of modular curves. Since the 1979, Shimura varieties have played a crucial
Arithmetic_geometry
Algebraic variety
quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular
Modular_curve
Modular form
Texts in Mathematics, No. 7, Springer-Verlag, 1978. ISBN 0-387-90040-3 Shimura, Goro, An Introduction to the Arithmetic Theory of Automorphic Functions
Cusp_form
Algebraic variety that is a moduli space for principally polarized abelian varieties
congruence subgroup of level n of a symplectic group. A Siegel modular variety may also be constructed as a Shimura variety defined by the Shimura datum associated
Siegel_modular_variety
In mathematics, a paramodular group is a special sort of arithmetic subgroup of the symplectic group. It is a generalization of the Siegel modular group
Paramodular_group
Australian-American mathematician
in Pure Mathematics, vol. XIX, American Mathematical Society, pp. 1–26 Shimura, Gorō (1971). Introduction to the Arithmetic Theory of Automorphic Functions
Frank_Calegari
Subgroup of the group of invertible n×n matrices
In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)
Linear_algebraic_group
Branch of mathematics
Rosenfeld, A. (1975) "Fuzzy graphs". In: Zadeh, L.A., Fu, K.S., Tanaka, K., Shimura, M. (eds.), Fuzzy Sets and their Applications to Cognitive and Decision
Fuzzy_mathematics
Westendorp. https://westy31.nl. Retrieved 29 March 2025. Elkies, N.D. (1998). "Shimura curve computations". In Buhler, J.P (ed.). Algorithmic Number Theory. ANTS
(2,3,7)_triangle_group
Theorem in abstract algebra
for the analytic theory of automorphic forms and for the arithmetic of Shimura varieties; it is the stabilized (or stable) trace formula, the reduction
Fundamental lemma (Langlands program)
Fundamental_lemma_(Langlands_program)
. (sequence A179982 in the OEIS) Hurwitz quaternion order Elkies, N.: Shimura curve computations. Algorithmic number theory (Portland, OR, 1998), 1–47
Hurwitz_surface
theoretical formulation of the theory of theta series in Weil (1964). The Shimura correspondence as constructed by Jean-Loup Waldspurger in Waldspurger (1980)
Theta_correspondence
Compact Riemann surface of genus 3
algebraic integers. The group Γ(I) is a subgroup of the (2,3,7) hyperbolic triangle group. Namely, Γ(I) is a subgroup of the group of elements of unit norm
Klein_quartic
Concept in mathematics
Hurwitz surfaces. The Hurwitz quaternion order was studied in 1967 by Goro Shimura, but first explicitly described by Noam Elkies in 1998. For an alternative
Hurwitz_quaternion_order
as the principal congruence subgroup of the (2,3,7) triangle group in a suitable tower of principal congruence subgroups. Here the choices of quaternion
MacBeath_surface
have the no small subgroup property. In a locally profinite group, a closed subgroup is locally profinite, and every compact subgroup is contained in an
Locally_profinite_group
Algebraic curve in mathematics
2 − s). In 1999 this was shown to be a consequence of the proof of the Shimura–Taniyama–Weil conjecture, which asserts that every elliptic curve over
Elliptic_curve
Canadian mathematician
quotient group, respectively; (b) earlier results of Martin Eichler and Goro Shimura in which the Hasse–Weil zeta functions of arithmetic quotients of the upper
Robert_Langlands
Unsolved problem in mathematics
conjectures was given by Michio Kuga with contributions from Mikio Sato, Goro Shimura, and Yasutaka Ihara, followed by Deligne (1971). The third statement followed
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Type of mathematical object
deformation theory of Galois representations was used in Wiles's work on the Shimura–Taniyama conjecture. Fundamental group scheme Geometric invariant theory
Group_scheme
generalization where one integrates the kernel function over non-diagonal subgroups. F is a global field, such as the field of rational numbers. A is the
Arthur–Selberg_trace_formula
Branch of number theory
to Hilbert's ninth problem. Around 1955, Japanese mathematicians Goro Shimura and Yutaka Taniyama observed a possible link between two apparently completely
Algebraic_number_theory
Pro-algebraic group
James S.; Ogus, Arthur; Shih, Kuang-yen (1982), Hodge cycles, motives, and Shimura varieties., Lecture Notes in Mathematics, vol. 900, Berlin-New York: Springer-Verlag
Serre_group
View of mathematicians to consolidate two or more theories into a more generalized one
correspondence between extensions of a field and subgroups of the field's Galois group. The Taniyama–Shimura conjecture for elliptic curves (now proven) establishes
Unifying theories in mathematics
Unifying_theories_in_mathematics
Mathematical law, a generalization of quadratic reciprocity
ideals (or ideles) to elements of a Galois group is trivial on a certain subgroup. Several more recent generalizations express reciprocity laws using cohomology
Reciprocity_law
French mathematician (1906-1998)
from Serge Lang (resp. of Jean-Pierre Serre) became known as the Taniyama–Shimura conjecture (resp. Taniyama–Weil conjecture) based on a roughly formulated
André_Weil
Linear operator acting on modular forms
')} with the sum taken over all the Λ ′ {\textstyle \Lambda '} that are subgroups of Λ {\textstyle \Lambda } of index n {\displaystyle n} . For example
Hecke_operator
British mathematician and logician
(and is a very natural setting for problems in) Diophantine geometry on Shimura varieties (Anand Pillay, Sergei Starchenko, Jonathan Pila) and representation
Angus_Macintyre
Branch of algebraic number theory concerned with abelian extensions
abelian extension corresponding to an open subgroup of finite index is called the class field for that subgroup, which gave the name to the theory. The fundamental
Class_field_theory
representation associated via the Jacquet–Langlands correspondence with f. Goro Shimura (1976) proved this formula, when k = Q {\displaystyle k=\mathbb {Q} } and
Waldspurger_formula
f^{6+\varepsilon }} . Zilber–Pink conjecture that if X {\displaystyle X} is a mixed Shimura variety or semiabelian variety defined over C {\displaystyle \mathbb {C}
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of smooth complex surface of kodaira dimension 0
{\displaystyle g\geq 2} ; it can be viewed as a Zariski open subset of a Shimura variety for the group SO(2,19). For each g, F g {\displaystyle {\mathcal
K3_surface
Mathematical conjectures in class field theory
Michael; Taylor, Richard (2001), The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University
Local_Langlands_conjectures
Mathematical group of loops in a Lie group
infinite-dimensional Lie group, with Lie algebra L𝔤 = C∞(S1, 𝔤). The subgroup ΩG of based loops is fundamental in homotopy theory, while central extensions
Loop_group
2015 EP by Super Junior-D&E
second extended play (EP) of South Korean pop duo Super Junior-D&E, a subgroup of the boy band Super Junior. The EP was released on April 1, 2015 under
Present_(Super_Junior-D&E_EP)
properties, such as functional equation, are still conjectural – the Taniyama–Shimura conjecture (which was proven in 2001) was just a special case, so that's
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
hypersurfaces Voisin, Hodge Theory and Complex Algebraic Geometry I, II Shimura curves within the locus of hyperelliptic Jacobians in genus three Period
Period_mapping
Prize awarded by the American Mathematical Society
fields I, II, III". 1972 Wolfgang M. Schmidt for various papers. 1977 Goro Shimura for various papers. 1982 Robert P. Langlands for pioneering work on automorphic
Cole_Prize
Graduate-level textbooks in mathematics
Theory of Lattice Subgroups Alexander Gorodnik, Amos Nevo 2009-10-11 160 9780691141855 173 On the Cohomology of Certain Non-Compact Shimura Varieties Sophie
Annals_of_Mathematics_Studies
Mathematical function
construct Arakelov Green functions for special divisors on orthogonal Shimura varieties. A complex-valued smooth function f {\displaystyle f} on the
Harmonic_Maass_form
Ancestral subkingdom of animals
Tsutomu; Watanabe, Yoko; Yasui, Kinya; Shi-cui, Zhang; Hori, Katsuji; Shimura, Yoshiro; Miyata, Takashi (July 1997). "An Estimate of Divergence Time
Parazoa
Unsolved problem in geometry
1007/s002080050333, MR 1731466, S2CID 119180172. Mumford, David (1969), "A Note of Shimura's paper "Discontinuous groups and abelian varieties"", Mathematische Annalen
Hodge_conjecture
Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor Taniyama–Shimura conjecture elliptic curves Now the modularity theorem for elliptic curves
List_of_conjectures
remain largely in the realm of conjecture, with the proof of the Taniyama–Shimura conjecture being a breakthrough. The Langlands philosophy is largely complementary
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
German mathematician (1896–1981)
1985, pp. 93–113, online and Publications list Goro Shimura: "1996 Steele Prizes" (with Shimura's reminiscences concerning C. L. Siegel), Notices of the
Carl_Ludwig_Siegel
Conjectures connecting number theory and geometry
Michael; Taylor, Richard (2001). The Geometry and Cohomology of Some Simple Shimura Varieties. Annals of Mathematics Studies. Vol. 151. Princeton University
Langlands_program
Special functions of several complex variables
functions". Osaka Journal of Mathematics. 32 (2): 431–450. ISSN 0030-6126. Shimura, On modular forms of half integral weight "Elliptic Integral Singular Value"
Theta_function
Geometric space whose points represent algebro-geometric objects of some fixed kind
variety. This is the problem underlying Siegel modular form theory. See also Shimura variety. Using techniques arising out of the minimal model program, moduli
Moduli_space
Algebraic structure
Milne, James (1982), "Tannakian categories", Hodge Cycles, Motives, and Shimura Varieties by Pierre Deligne, James S. Milne, Arthur Ogus, Kuang-yen Shih
Hodge_structure
Verdier, Sur les intégrales attachées aux formes automorphes, d'après Shimura (automorphic forms) François Bruhat, Travaux de Sternberg (classical mechanics)
Séminaire Nicolas Bourbaki (1960–1969)
Séminaire_Nicolas_Bourbaki_(1960–1969)
des groupes de Lie, d'après Cartan, Iwasawa et Mostow (maximal compact subgroups) Henri Cartan, Espaces fibrés analytiques complexes (analytic geometry
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
Songs recorded by South Korean boyband, Super Junior
concept "separately and together" in their musical activities by forming subgroups which focuses on different genres; Super Junior-K.R.Y. which focuses on
List of songs recorded by Super Junior
List_of_songs_recorded_by_Super_Junior
SHIMURA SUBGROUP
SHIMURA SUBGROUP
Female
Hebrew
(ש×ִירָה) Hebrew name SHIRA means "song."
Girl/Female
Indian
Ready for battle
Female
Russian
(Шура) Short form of Russian unisex Sashura, SHURA means "defender of mankind." Compare with another form of Shura.
Boy/Male
Greek Latin
Slew Chimera.
Female
Japanese
(é™é¦™) Japanese name SHIZUKA means "quiet."
Male
Russian
(Шура) Short form of Russian unisex Sashura, SHURA means "defender of mankind." Compare with strictly feminine Shura.
Girl/Female
Egyptian
Grateful.
Male
English
Anglicized form of Hebrew Shimiy, SHIMEA means "famous, renowned." In the bible, this is the name of many characters, including a Reubenite, son of Gog and father of Micah.
Girl/Female
Arabic, Muslim
Diamond
Female
Native American
Native American Navajo name SHIMA means "mother."
Female
Hebrew
(ש×וּרָה) Hebrew name SHURA means "row, line." Compare with another form of Shura.
Female
Hebrew
(ש×ָמִירָה) Feminine form of Hebrew Shamiyr, SHAMIRA means "a sharp point," hence "thorn."Â
Girl/Female
Indian, Sanskrit
Star
Boy/Male
Greek
The monster killed by Bellerophon.
Girl/Female
Hindu
A flower
Girl/Female
Arabic
Very Thankful
Girl/Female
Hindu
Gift of God
Girl/Female
Arabic, British, Russian
Battle Ready Warrior
Female
Hebrew
(ש×ִפְרָה) Variant spelling of Hebrew Shiphrah, SHIFRA means "beauty, brightness." Compare with another form of Shifra.
Girl/Female
Muslim
Ready for battle
SHIMURA SUBGROUP
SHIMURA SUBGROUP
Boy/Male
Norse
God of poetry.
Female
Egyptian
, the wife and daughter of Rameses-Miamun.
Girl/Female
German, Latin
Old; Prosperous; Small Winged One
Boy/Male
Indian
Lion, Lord of mount Kailash or Lord Shiva
Biblical
station;
Boy/Male
Hindu, Indian
King
Girl/Female
Czechoslovakian
Girl/Female
French
Crowned with laurels.
Boy/Male
African, American, Anglo, Australian, British, Christian, English
From the Town by the Lake
Boy/Male
American, Australian, British, Chinese, English, Irish
Broad Hillside
SHIMURA SUBGROUP
SHIMURA SUBGROUP
SHIMURA SUBGROUP
SHIMURA SUBGROUP
SHIMURA SUBGROUP
n.
The restless flycatcher (Seisura inquieta) of Australia; -- called also restless thrush and volatile thrush. It makes a noise like a scissors grinder, to which the name alludes.
pl.
of Chimera
n.
A monster represented as vomiting flames, and as having the head of a lion, the body of a goat, and the tail of a dragon.
n.
A subdivision of a group, as of animals.
n.
A vain, foolish, or incongruous fancy, or creature of the imagination; as, the chimera of an author.