Abelian and derived deformations in the presence of Z-generating geometric helices

Details Abelian and derived deformations in the presence of Z-generating geometric helices Abelian and derived deformations in the presence of Z-generating geometric helices

2010-01-24

arxiv.org/abs/1001.4265v3

Mathematics

Algebraic Geometry

21 pages

Scientific paper

For a Grothendieck category C which, via a Z-generating sequence (O(n))_{n in 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 in 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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