The curvature problem for formal and infinitesimal deformations

Michel Van den Bergh; Wendy Lowen

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

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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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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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