Chern classes of automorphic vector bundles, II

  title={Chern classes of automorphic vector bundles, II},
  author={H'elene Esnault and Michael Harris},
  journal={arXiv: Algebraic Geometry},
  • H'elene Esnault, Michael Harris
  • Published 2017
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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.