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- Shimura_variety abstract "In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. The term "Shimura variety" applies to the higher-dimensional case, in the case of one-dimensional varieties one speaks of Shimura curves. Hilbert modular surfaces and Siegel modular varieties are among the best known classes of Shimura varieties.Special instances of Shimura varieties were originally introduced by Goro Shimura in the course of his generalization of the complex multiplication theory. Shimura showed that while initially defined analytically, they are arithmetic objects, in the sense that they admit models defined over a number field, the reflex field of the Shimura variety. In the 1970s, Pierre Deligne created an axiomatic framework for the work of Shimura. Around the same time Robert Langlands remarked that Shimura varieties form a natural realm of examples for which equivalence between motivic and automorphic L-functions postulated in the Langlands program can be tested. Automorphic forms realized in the cohomology of a Shimura variety are more amenable to study than general automorphic forms; in particular, there is a construction attaching Galois representations to them.".
- Shimura_variety wikiPageExternalLink catalogue.asp?ISBN=9780521004190.
- Shimura_variety wikiPageExternalLink Harmonic_Analysis.
- Shimura_variety wikiPageExternalLink 2005aX.pdf.
- Shimura_variety wikiPageExternalLink eightfold.html.
- Shimura_variety wikiPageExternalLink index.html.
- Shimura_variety wikiPageExternalLink item?id=SB_1970-1971__13__123_0.
- Shimura_variety wikiPageID "10389861".
- Shimura_variety wikiPageRevisionID "602943567".
- Shimura_variety first "J.S.".
- Shimura_variety hasPhotoCollection Shimura_variety.
- Shimura_variety id "s/s110090".
- Shimura_variety last "Milne".
- Shimura_variety subject Category:Algebraic_geometry.
- Shimura_variety subject Category:Automorphic_forms.
- Shimura_variety subject Category:Zeta_and_L-functions.
- Shimura_variety type Abstraction100002137.
- Shimura_variety type AutomorphicForms.
- Shimura_variety type Form106290637.
- Shimura_variety type LanguageUnit106284225.
- Shimura_variety type Part113809207.
- Shimura_variety type Relation100031921.
- Shimura_variety type Word106286395.
- Shimura_variety comment "In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. The term "Shimura variety" applies to the higher-dimensional case, in the case of one-dimensional varieties one speaks of Shimura curves.".
- Shimura_variety label "Shimura variety".
- Shimura_variety label "志村多様体".
- Shimura_variety label "志村簇".
- Shimura_variety sameAs 志村多様体.
- Shimura_variety sameAs m.02qb9nz.
- Shimura_variety sameAs Q7497063.
- Shimura_variety sameAs Q7497063.
- Shimura_variety sameAs Shimura_variety.
- Shimura_variety wasDerivedFrom Shimura_variety?oldid=602943567.
- Shimura_variety isPrimaryTopicOf Shimura_variety.