Joint IAS/Princeton University Number Theory Seminar

In this talk we will explain how to attach Galois representations to certain Hecke eigenforms in the coherent cohomology of good reduction Shimura varieties. As an application we will give a new proof of cases of a recent theorem of Scholze attaching Galois representations to certain torsion classes in the cohomology of arithmetic locally symmetric spaces. The main tool will be some "generalized Hasse invariants" on the Ekedahl-Oort strata of the special fiber of the Shimura variety.