Hochschild cohomology of abelian categories and ringed spaces
Hochschild cohomology of abelian categories and ringed spaces
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DOI：
10.1016/j.aim.2004.11.010
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发表时间：
2004-05
影响因子：
1.7
通讯作者：
Wendy Lowen;M. Bergh
中科院分区：
文献类型：
--
作者：
Wendy Lowen;M. Bergh
本文继续发展了作者在前一篇文章中介绍的阿贝尔范畴的变形理论。我们首先表明，阿贝尔范畴的变形理论是由一个障碍理论控制的一个合适的概念Hochschild上同调阿贝尔范畴。然后，我们表明，这Hochschild上同调相吻合的一个定义的Gerstenhaber，Schack和天鹅的情况下，模块类别的图和计划，也与Hochschild上同调的确切类别最近推出的凯勒。此外，我们表明在完整的一般性，Hochschild上同调满足迈耶-Vietoris性质，并为不断环空间，它符合上同调的结构层。
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.