Publication
Title
Hochschild cohomology of abelian categories and ringed spaces
Author
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 MayerVietoris property and that for constantly ringed spaces it coincides with the cohomology of the structure sheaf.
Language
English
Source (journal)
Advances in mathematics. - New York, N.Y.
Publication
New York, N.Y. : 2005
ISSN
0001-8708
Volume/pages
198:1(2005), p. 172-221
ISI
000233780400009
Full text (Publisher's DOI)
UAntwerpen
 Faculty/Department Publication type Subject