Integral canonical models for automorphic vector bundles of abelian type

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 ${\mathcal{O}}_E\left[1∕N\right]$ for Shimura varieties of abelian type with hyperspecial level at all primes not dividing $N$ 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.