Deformation theory of abelian categories

Lowen, Wendy; Van den Bergh, Michel

doi:10.1090/S0002-9947-06-03871-2

Deformation theory of abelian categories
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by Wendy Lowen and Michel Van den Bergh PDF

Trans. Amer. Math. Soc. 358 (2006), 5441-5483 Request permission

Abstract:

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations, and we construct several equivalences between deformation problems.

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