## Hélène Esnault ; Michel Harris - Chern classes of automorphic vector bundles, II

epiga:4238 - Épijournal de Géométrie Algébrique, October 24, 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.4238
Chern classes of automorphic vector bundles, II

Authors: Hélène Esnault ; Michel Harris

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.

Volume: Volume 3
Published on: October 24, 2019
Submitted on: January 26, 2018
Keywords: Mathematics - Algebraic Geometry