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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2021

Title: Hochschild cohomology of abelian categories and ringed spaces
Authors: Lowen, M
VAN DEN BERGH, Michel
Issue Date: 2005
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: ADVANCES IN MATHEMATICS, 198(1). p. 172-221
Abstract: This paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors. We show first that the deformation theory of abelian categories is controlled by an obstruction theory in terms of a suitable notion of Hochschild cohomology for abelian categories. We then show that this Hochschild cohomology coincides with the one defined by Gerstenhaber, Schack and Swan in the case of module categories over diagrams and schemes and also with the Hochschild cohomology for exact categories introduced recently by Keller. In addition we show in complete generality that Hochschild cohomology satisfies a Mayer-Vietoris property and that for constantly ringed spaces it coincides with the cohomology of the structure sheaf. (c) 2005 Elsevier Inc. All rights reserved.
Notes: Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium. Vrije Univ Brussels, Dept DWIS, B-1050 Brussels, Belgium.Van den Bergh, M, Limburgs Univ Ctr, Dept WNI, Univ Campus,Bldg D, B-3590 Diepenbeek, Belgium.wlowen@vub.ac.be vdbergh@luc.ac.be
URI: http://hdl.handle.net/1942/2021
DOI: 10.1016/j.aim.2004.11.010
ISI #: 000233780400009
ISSN: 0001-8708
Category: A1
Type: Journal Contribution
Validation: ecoom, 2006
Appears in Collections: Research publications

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