The HKR isomorphism and Hochschild cohomology

Abstract: For a smooth scheme X, the HKR isomorphism identifies the Hochschild cohomology of X with the cohomology of polyvector fields as vector spaces. This isomorphism is known as the classical HKR isomorphism for the diagonal embedding: X in X\timesX. We discuss the generalization of the HKR isomorphism to arbitrary closed embeddings and the corresponding functoriality property. Then we recall the generalization of the HKR isomorphism to orbifolds. We apply all the results above to study the product structure of orbifold Hochschild cohomology.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09

Meeting ID: 918 7552 8987 Password: LAGOON2022

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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