Integral models for Shimura varieties of abelian type

Integral Models for Shimura Varieties of Abelian Type

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...

Abelian varieties arising from Mumford’s Shimura curves

In this paper, we study abelian varieties of dimension 4 over number fields with the property that the Lie algebra of their Mumford–Tate group is C-isomorphic to Ga (sl2)3. Such abelian varieties occur naturally as fibres of universal families of abelian varieties over Shimura curves associated to algebraic groups over Q that are C-isomorphic to (SL2) 3. We study the reductionsmodulo prime idea...

Compactifications 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.)

Models of Shimura varieties in mixed characteristic

Descent for Shimura Varieties

Wildeshaus and others have pointed out to me that it is not obvious that the descent maps on a Shimura variety given by Langlands’s Conjugacy Conjecture (Langlands 1979, Section 6) satisfy the continuity condition required for the descent to be effective. The following provides one proof of this (maybe not the best). Since the family (fσ) satisfying the conditions (a,b,c) below is unique (by th...