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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A Hochschild cohomology comparison theorem for prestacks

Authors: Wendy Lowen and Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 363 (2011), 969-986
MSC (2000): Primary 16E40, 18D30
Published electronically: September 21, 2010
MathSciNet review: 2728592
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Abstract: We generalize and clarify Gerstenhaber and Schack's ``Special Cohomology Comparison Theorem''. More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category $ \mathcal{U}$ and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not have to assume that $ \mathcal{U}$ is a poset.

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Wendy Lowen
Affiliation: Departement Wiskunde-Informatica, University of Antwerpen, Middelheimcampus, Middelheimlaan 1, 2020 Antwerp, Belgium

Michel Van den Bergh
Affiliation: Department WNI, Hasselt University, Agoralaan, 3590 Diepenbeek, Belgium

Keywords: Hochschild cohomology, fibered categories, special cohomology comparison theorem
Received by editor(s): May 31, 2009
Published electronically: September 21, 2010
Additional Notes: The first author is a postdoctoral fellow with the Fund of Scientific Research Flanders (FWO)
The second author is a director of research at the FWO
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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