# Hochschild cohomology of Azumaya algebras

SPEAKER: Vadim Vologodsky

TITLE: Hochschild cohomology of Azumaya algebras

ABSTRACT: Let X be a smooth algebraic variety over a field k of prime characteristic. Assuming that the characteristic of k is greater than twice the dimension of X, I will show that the Hochschild cohomology of the sheaf of differential operators on X is canonically isomorphic to the de Rham cohomology of the cotangent scheme of X.