Integral canonical models of exceptional Shimura varieties

TL;DR

This paper establishes the existence of integral canonical models for exceptional Shimura varieties at large primes, extending previous results and deriving several important arithmetic and geometric consequences.

Contribution

It proves the existence of integral canonical models for a broad class of Shimura varieties, including exceptional types, and introduces new applications in arithmetic geometry.

Findings

Existence of integral canonical models for exceptional Shimura varieties.

Extension of Kisin-Kottwitz results to more general cases.

Derivation of new arithmetic and geometric consequences.

Abstract

We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of integral canonical models for images of period maps corresponding to geometric families. We deduce several consequences from this, including an unramified rigid analogue of Borel's extension theorem, a version of Tate semisimplicity, CM lifting theorems, and a weakened version of Tate's isogeny theorem for ordinary points.