Wendy Lowen

Obstruction Theory for Objects in Abelian and Derived Categories

ABSTRACT In this article, we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Ext-groups. In an appendix we prove the existence of miniversal derived deformations of complexes.

Algebroid prestacks and deformations of ringed spaces

For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules (Lowen and Van den Bergh, 2006) are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. It follows in particular that there is a deformation equivalence between Mod(O) and Qch(O).

A Hochschild cohomology comparison theorem for prestacks

[Lowen, Wendy] Univ Antwerp, Dept Wiskunde Informat, B-2020 Antwerp, Belgium. [Van den Bergh, Michel] Hasselt Univ, Dept WNI, B-3590 Diepenbeek, Belgium.

Non-commutative deformations and quasi-coherent modules

We identify a class of quasi-compact semi-separated (qcss) twisted presheaves of algebras

Tensor functional topology

\mathcal {A}

A generalization of the Gabriel–Popescu theorem

A for which well-behaved Grothendieck abelian categories of quasi-coherent modules

Hochschild cohomology, the characteristic morphism and derived deformations

\mathsf {Qch} (\mathcal {A})