Galois deformations and arithmetic geometry of Shimura varieties
نویسنده
چکیده
Shimura varieties are arithmetic quotients of locally symmetric spaces which are canonically defined over number fields. In this article, we discuss recent developments on the reciprocity law realized on cohomology groups of Shimura varieties which relate Galois representations and automorphic representations. Focus is put on the control of -adic families of Galois representations by -adic families of automorphic representations. Arithmetic geometrical ideas and methods on Shimura varieties are used for this purpose. A geometrical realization of the Jacquet–Langlands correspondence is discussed as an example. Mathematics Subject Classification (2000). 11F55, 11F80, 11G18.
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Tetsushi Ito (Kyoto University, Graduate School of Science, Assistant Professor) 【Outline of survey】 Shimura varieties are algebraic varieties (geometric objects defined by equations), which are generalizations of modular curves. Previously, several mathematical objects in arithmetic geometry, Galois representations, automorphic representations were studied from individual perspectives. However...
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