Integral Models for Shimura Varieties of Abelian Type
نویسندگان
چکیده
Introduction 967 1. Reductive groups and p-divisible groups 971 (1.1) Cocharacters and filtrations 971 (1.2) Review of S-modules 973 (1.3) Reductive groups and crystalline representations 975 (1.4) Application to p-divisible groups 978 (1.5) Deformation theory 981 2. Integral canonical models of Hodge type 986 (2.1) Shimura varieties 986 (2.2) Absolute Hodge cycles 989 (2.3) Integral models 992 3. Integral canonical models of abelian type 995 (3.1) Twisting abelian varieties 995 (3.2) The action of G(Q) 997 (3.3) Connected Shimura varieties 1001 (3.4) Integral models II 1005 References 1011
منابع مشابه
Special Cycles on Unitary Shimura Varieties I. Unramified Local Theory
A relation between a generating series constructed from arithmetic cycles on an integral model of a Shimura curve and the derivative of a Siegel Eisenstein series of genus 2 was established by one of us in [9]. There, the hope is expressed that such a relation should hold in greater generality for integral models of Shimura varieties attached to orthogonal groups of signature (2, n − 2) for any...
متن کاملCompactifications of Splitting Models of Pel-type Shimura Varieties
We construct toroidal and minimal compactifications, with expected properties concerning stratifications and formal local structures, for all integral models of PEL-type Shimura varieties defined by taking normalizations over the splitting models considered by Pappas and Rapoport. (These include, in particular, all the normal flat splitting models they considered.)
متن کاملOn the Conjecture of Langlands and Rapoport
FORENOTE (2007): The remarkable conjecture of Langlands and Rapoport (1987) gives a purely group-theoretic description of the points on a Shimura variety modulo a prime of good reduction. In an article in the proceedings of the 1991 Motives conference (Milne 1994, §4), I gave a heuristic derivation of the conjecture assuming a sufficiently good theory of motives in mixed characteristic. I wrote...
متن کاملLocal Models of Shimura Varieties and a Conjecture of Kottwitz
We give a group theoretic definition of “local models” as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are ob...
متن کاملThe 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 کامل