Geometric Satake, categorical traces, and arithmetic of Shimura varieties
نویسندگان
چکیده
منابع مشابه
The geometric and arithmetic volume of Shimura varieties of orthogonal type
We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the well-known computation of their geometric volume by induction, using special cycles. A functorial theory of integral models of toroidal compactifications of those varieties and a theory of arithmeti...
متن کاملGalois deformations and arithmetic geometry of Shimura varieties
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 fami...
متن کاملThe arithmetic volume of Shimura varieties of orthogonal type
The overall aim of this thesis is to compute arithmetic volumes of Shimura varieties of orthogonal type and natural heights of the special cycles on them. We develop a general theory of integral models of toroidal compactifications of Shimura varieties of Hodge type (and of its standard principal bundle) for the case of good reduction. This enables us, using the theory of Borcherds products, an...
متن کاملParametrizing Shimura Subvarieties of A1 Shimura Varieties and Related Geometric Problems
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b = (H ) × (H). A special case describes all Shimura subvarieties of type A1 Shimura varieties. We produce, for any n ≥ 1, examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura sub...
متن کاملShimura Varieties: the Geometric Side of the Zeta Function
These are my notes for four talks at the Institute for Advanced Study, February 21,23,28, and March 2, 1995. Appearances to the contrary, they are rough notes. After giving a brief introduction to Shimura varieties, and in particular explaining how to realize them as moduli varieties, we give a heuristic derivation of a formula for the number of points on the reduction of a Shimura variety with...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2016
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2016.v2016.n1.a4