Hochschild cohomology of abelian categories and ringed spaces
By Wendy Lowen, Michel van den Bergh. 2004
129 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ecec766ebeebdfb8c17950a6c9a255d5d579da8a
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In Algebra and Number Theory
- Michel van den Bergh
- Wendy Lowen
- Osamu Iyama
- Tatiana Gateva-Ivanova
- Raf Bocklandt
- Nathan Broomhead
- Lingyan Guo
- Leandro Vendramin
In Geometry and Topology
- Michel van den Bergh
- Wendy Lowen
- Yukinobu Toda
- Osamu Iyama
- Tatiana Gateva-Ivanova
- Markus Reineke
- Raf Bocklandt
- B. Keller
In Mathematical Physics
- Michel van den Bergh
- Wendy Lowen
- Yukinobu Toda
- Markus Reineke
- Daisuke Yamakawa
- Osamu Iyama
- Dmitri Orlov
- Bertrand Toën
Citations in the corpus
- Deformation theory of abelian categories (2004, methodology): “In a subsequent paper [17] we will develop the corresponding obstruction theory in terms of a suitable notion of Hochschild cohomology.”