Regular integral models for Shimura varieties of orthogonal 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...

The 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...

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

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...