Partial Hasse invariants for Shimura varieties of Hodge-type

Abstract

For a connected reductive group $G$ over a finite field, we define partial Hasse invariants on the stack of $G$-zip flags. We obtain similar sections on the flag space of Shimura varieties of Hodge-type. They are mod $p$ automorphic forms which cut out a single codimension one stratum. We study their properties and show that such invariants admit a natural factorization through higher rank automorphic vector bundles. We define the socle of an automorphic vector bundle, and show that partial Hasse invariants lie in this socle.

38 pages

References in corpus (4)

• Minimal weights of Hilbert modular forms in characteristic p
• The cone of minimal weights for mod $p$ Hilbert modular forms
• Globally Irreducible Weyl Modules
• Automorphic vector bundles on the stack of $G$-zips