Topic
Shimura variety
About: Shimura variety is a research topic. Over the lifetime, 881 publications have been published within this topic receiving 23175 citations.
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Book•
01 Nov 2008
TL;DR: Modular forms, elliptic curves, and modular curves as Riemann surfaces have been used to define the Eichler-Shimura Relation and L-functions.
Abstract: Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.
853 citations
Book•
08 Oct 2014
TL;DR: In this article, Langlands's construction of the Taniyama Group is described, as well as the construction of a Taniya Group for Hodge Cycles on Abelian Varieties.
Abstract: General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands's Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.- Addendum 1989.- General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands's Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.
814 citations
Book•
22 Dec 1995
TL;DR: In this paper, the relation of "p"-adic period domains to moduli space of arbitrary reductive groups is investigated, and nonarchimedean uniformization theorems for general Shimura varieties are established.
Abstract: In this monograph "p"-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of "p"-adic period domains to moduli space of "p"-divisible groups is investigated. In addition, non-archimedean uniformization theorems for general Shimura varieties are established.The exposition includes background material on Grothendieck's "mysterious functor" (Fontaine theory), on moduli problems of "p"-divisible groups, on rigid analytic spaces, and on the theory of Shimura varieties, as well as an exposition of some aspects of Drinfelds' original construction. In addition, the material is illustrated throughout the book with numerous examples.
555 citations
537 citations