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Hochschild cohomology parametrizes curved Morita deformations

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arxiv 2406.04945 v2 pith:OTGCFNEG submitted 2024-06-07 math.KT

Alessandro Lehmann This is my paper · ORCID
classification math.KT
keywords deformationscurvedcohomologyequivalencehochschildinducesmoritaalgebra
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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.

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  1. Deformations of triangulated categories with t-structures via derived injectives

    math.CT 2024-11 conditional novelty 7.0 of 10

    Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.

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