Title
Abelian and derived deformations in the presence of ℤ-generating geometric helices Abelian and derived deformations in the presence of ℤ-generating geometric helices
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Journal of noncommutative geometry
Volume/pages
5(2011) :4 , p. 477-505
ISSN
1661-6952
ISI
000295822400001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
For a Grothendieck category C which, via a Z -generating sequence (O(n)) n∈Z , is equivalent to the category of quasi-coherent modules over an associated Z -algebra a , we show that under suitable cohomological conditions taking quasi-coherent modules defines an equivalence between linear deformations of a and abelian deformations of C . If (O(n)) n∈Z is at the same time a geometric helix in the derived category, we show that restricting a (deformed) Z -algebra to a thread of objects defines a further equivalence with linear deformations of the associated matrix algebra
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