# Chern classes of automorphic vector bundles, II

@article{Esnault2017ChernCO, title={Chern classes of automorphic vector bundles, II}, author={H'elene Esnault and Michael Harris}, journal={arXiv: Algebraic Geometry}, year={2017} }

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.

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