Hochschild cohomology parametrizes curved Morita deformations

2024/06/07 by Alessandro Lehmann · 1 voice
Mathematics · #math.KT

paper · pdf · doi:10.1090/proc/17133

arxiv published 2024/06/07 · arxiv updated 2025/03/03

Abstract

We show that, if one allows for curved deformations, the canonical map introduced in [KL09] between Morita deformations and second Hochschild cohomology of a dg algebra becomes a bijection. We also show that a bimodule induces an equivalence of curved deformations precisely when it induces an equivalence between the respective 1-derived categories. These results, together with arXiv:2402.08660, solve the curvature problem for first order deformations.

Citations

• Filtered derived categories of curved deformations

Discussions

• Alessandro Lehmann Hochschild cohomology parametrizes curved Morita deformations https://arxiv.org/abs/2406.04945 [bsky, 0 points, 0 comments]

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