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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.