Automorphic vector bundles on the stack of $G$-zips

Abstract

For a connected reductive group $G$ over a finite field, we study automorphic vector bundles on the stack of $G$-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the Brylinski--Kostant filtration. Moreover, we give an equivalence of categories between the category of automorphic vector bundles on the stack of $G$-zips and a category of admissible modules with actions of a zero-dimensional algebraic subgroup a Levi subgroup and monodromy operators.

33 pages

References in corpus (5)

• Cycles on Shimura varieties via geometric Satake
• Discrete invariants of varieties in positive characteristic
• EKOR strata for Shimura varieties with parahoric level structure
• Normalization of closed Ekedahl-Oort strata
• Weights of mod $p$ automorphic forms and partial Hasse invariants

Cited by in corpus (1)

• Partial Hasse invariants for Shimura varieties of Hodge-type