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arXiv · 2210.02111

Twisted equivariant HKR theorem for torus action and the small quantum group

Nicolas Hemelsoet
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Abstract

We show that when a torus $T$ acts on a smooth variety $X$, the twisted HKR isomorphism is equivariant. The main consequence is that the Bezrukavnikov- Lachowska isomorphism, relating the Hochschild cohomology of the principal block of the small quantum group to certain sheaf cohomology groups on the Springer resolution $\widetilde{\mathcal{N}}$ , can be upgraded to a ring isomorphism by a twist.

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Nicolas Hemelsoet. 2022-10-05. Twisted equivariant HKR theorem for torus action and the small quantum group. https://arxiv.org/abs/2210.02111

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