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Hochschild Cohomology of Torus Equivariant D-modules
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Abstract
We discuss the Hochschild cohomology of the category of D-modules associated to an algebraic stack. In particular we describe the Hochschild cohomology of the category of torus-equivariant D-modules as the cohomology of a D-module on the loop space of the quotient stack. Finally, we give an approach for understanding the Hochschild cohomology of D-modules on general stacks via a relative compactification of the diagonal. This work is motivated by a desire to understand the support theory (in the sense of [6]) of D-modules on stacks.
Title: Hochschild Cohomology of Torus Equivariant D-modules
Description:
Abstract
We discuss the Hochschild cohomology of the category of D-modules associated to an algebraic stack.
In particular we describe the Hochschild cohomology of the category of torus-equivariant D-modules as the cohomology of a D-module on the loop space of the quotient stack.
Finally, we give an approach for understanding the Hochschild cohomology of D-modules on general stacks via a relative compactification of the diagonal.
This work is motivated by a desire to understand the support theory (in the sense of [6]) of D-modules on stacks.
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