Integral canonical models for automorphic vector bundles of abelian type (Q1677806)

This article defines and constructs integral canonical models for Shimura varieties of abelian type, as well as for the automorphic vector bundles lying over them. These models are defined over $\mathcal{O}_E[1/N]$, where $E$ is the reflex field and $N$ is such that the underlying group $G$ admits a reductive model over $\mathbb{Z}[1/N]$. The approach builds heavily off earlier work of Kisin, who constructed local integral models for the Shimura varieties themselves. The canonicity of the new models means that they localize to Kisin's models, but more work is needed to show that these local models glue to something global that can be characterized uniquely. \par These constructions should have applications to many problems in automorphic forms and arithmetic, especially $p$-adic methods for which working with canonical integral models is often crucial.