UC Berkeley

We partially extend the results of [8] by constructing Hasse invariants on good reductions of proper abelian type Shimura varieties, and using them to associate Galois representations to systems of Hecke eigenvalues. This is made possible by (1) using the Grifths bundle, as described by Goldring in [7], as a generalization of the Hodge line bundle, and (2) using the abelian type Ekedahl-Oort stratifcation constructed by Shen and Zhang in [26] and independently by Imai, Kato, and Youcis in [10]. Our main contribution is utilizing these constructions together under the main ideas of [8].