Hochschild cohomology parametrizes curved Morita deformations
K-Theory and Homology
2025-03-05 v2
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.
Cite
@article{arxiv.2406.04945,
title = {Hochschild cohomology parametrizes curved Morita deformations},
author = {Alessandro Lehmann},
journal= {arXiv preprint arXiv:2406.04945},
year = {2025}
}
Comments
13 pages, no figures. v2: improved exposition and fixed several typos. To appear in Proceedings of the AMS