Chern classes of automorphic vector bundles, II

TL;DR

This paper proves that certain algebraic invariants called $ ext{ell}$-adic Chern classes of automorphic vector bundles on Shimura varieties descend to minimal compactifications and are Galois-invariant, enhancing understanding of their arithmetic properties.

Contribution

It establishes the descent and Galois invariance of $ ext{ell}$-adic Chern classes for automorphic vector bundles on Shimura varieties of Hodge type.

Findings

$ ext{ell}$-adic Chern classes descend to minimal compactifications

Chern classes are Galois-invariant

Results apply to Shimura varieties over $ar{ ext{Q}}_p$

Abstract

We prove that the $\ell$-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$-adic cohomology of the minimal compactifications. These are invariant under the Galois group of the $p$-adic field above which the variety and the bundle are defined.