Integral Canonical Models for Automorphic Vector Bundles of Abelian Type

TL;DR

This paper constructs integral canonical models for automorphic vector bundles over Shimura varieties of abelian type, extending Kisin's work and providing a foundation for further arithmetic and geometric applications.

Contribution

It introduces a new framework for integral canonical models of automorphic vector bundles on abelian type Shimura varieties, building on and extending Kisin's constructions.

Findings

Constructed integral canonical models over rings of integers with finitely many primes inverted.

Defined and constructed integral canonical models for standard principal bundles.

Derived integral models for automorphic vector bundles from principal bundle models.

Abstract

We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number fields with finitely many primes inverted for Shimura varieties of abelian type with hyperspecial level at all primes we do not invert, compatible with Kisin's construction. We then define a notion of an integral canonical model for the standard principal bundles lying over Shimura varieties and proceed to construct them in the abelian type case. With these in hand, one immediately also gets integral models for automorphic vector bundles.