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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Deformation theory of abelian categories


Authors: Wendy Lowen and Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 358 (2006), 5441-5483
MSC (2000): Primary 13D10, 14A22, 18E15
Published electronically: July 21, 2006
MathSciNet review: 2238922
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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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Additional Information

Wendy Lowen
Affiliation: Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
Email: wlowen@vub.ac.be

Michel Van den Bergh
Affiliation: Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium
Email: vdbergh@luc.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03871-2
PII: S 0002-9947(06)03871-2
Received by editor(s): September 24, 2004
Received by editor(s) in revised form: October 7, 2004
Published electronically: July 21, 2006
Additional Notes: The first author is a Postdoctoral Fellow of the Research Foundation–Flanders (FWO)
The second author is a senior researcher at the FWO
Article copyright: © Copyright 2006 American Mathematical Society