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Mathematics > Algebraic Geometry

arXiv:1807.09268 (math)
[Submitted on 24 Jul 2018 (v1), last revised 31 Jul 2018 (this version, v2)]

Title:Hochschild cohomology and group actions

Authors:Alexander Perry
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Abstract:Given a finite group action on a (suitably enhanced) triangulated category linear over a field, we establish a formula for the Hochschild cohomology of the category of invariants, assuming the order of the group is coprime to the characteristic of the base field. The formula shows that the cohomology splits canonically with one summand given by the invariant subspace of the Hochschild cohomology of the original category. We also prove that Serre functors act trivially on Hochschild cohomology, and combine this with our formula to give a useful mechanism for computing the Hochschild cohomology of fractional Calabi-Yau categories.
Comments: 21 pages, minor updates. This is a revised and expanded version of what was originally an appendix to arXiv:1605.06568v1
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.09268 [math.AG]
  (or arXiv:1807.09268v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.09268

Submission history

From: Alexander Perry [view email]
[v1] Tue, 24 Jul 2018 22:23:11 UTC (19 KB)
[v2] Tue, 31 Jul 2018 05:06:35 UTC (20 KB)
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