Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations

Abstract

We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some "generalized Hasse invariants" adapted to the Ekedahl-Oort stratification of the special fiber.

This is the author's PhD Thesis. Comments and corrections welcome!

References in corpus (1)

• Introduction to Shimura varieties with bad reduction of parahoric type

Cited by in corpus (12)

• Tautological rings of Shimura varieties and cycle classes of Ekedahl-Oort strata
• Generalized mu-ordinary Hasse invariants
• Coherent cohomology of Shimura varieties and automorphic forms
• The weight reduction of mod $p$ Siegel modular forms for $GS{p}_4$
• Minimal modularity lifting for non-regular symplectic representations
• Normalization of closed Ekedahl-Oort strata
• A quotient of the Lubin-Tate tower II
• Automorphic vector bundles with global sections on $G$-${\mathtt{Zip}}^{\mathcal{Z}}$-schemes
• Arithmetic Satake compactifications and algebraic Drinfeld modular forms
• Higher Hida theory for Hilbert modular varieties in the totally split case
• Unramifiedness of Galois representations arising from Hilbert modular surfaces
• Lifting Chern classes by means of Ekedahl-Oort strata