Principal bundles on toroidal compactifications of integral canonical models of abelian-type Shimura varieties

TL;DR

This paper constructs canonical extensions of principal bundles on toroidal compactifications of integral models of abelian-type Shimura varieties, advancing the understanding of their geometric and arithmetic structures.

Contribution

It introduces a method to extend principal bundles canonically on toroidal compactifications of integral canonical models of abelian-type Shimura varieties.

Findings

Canonical extensions of principal bundles are constructed.

Extensions are compatible with the compactification structure.

Results facilitate further study of Shimura varieties' arithmetic properties.

Abstract

In this paper, we construct canonical extensions of principal $\mathcal{G}^c$- (and $M^c$-)bundles on toroidal compactifications of integral canonical models of abelian-type Shimura varieties with hyperspecial levels.