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The curvature problem for formal and infinitesimal deformations

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arxiv 1505.03698 v2 pith:EEZZ6FCL submitted 2015-05-14 math.KT

Wendy Lowen , Michel Van den Bergh This is my paper · ORCID
classification math.KT
keywords deformationscurvaturecurvedelementsformalinfinitesimalmaurer-cartanmorita
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We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This solves the "curvature problem", i.e. the phenomenon that such Maurer-Cartan elements naturally parameterize curved A_infinity deformations. In the infinitesimal setup, we show how (n+1)-th order curved deformations give rise to n-th order uncurved Morita deformations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Monoidal structures arising from $B_\infty$-algebras with applications to Hopf algebras

    math.RT 2026-08 conditional novelty 8.0 of 10

    A B-infinity structure on an algebra gives a monoidal tensor product on the derived category of right modules, and for Hopf algebras this produces an algebraic proof of the Benson-Krause monoidal equivalence.

  2. 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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