Deformations of modules through butterflies and gerbes

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Herr, Leo¹ 

[1] Univ Colorado, Boulder, CO 80309 USA

关键词: Deformations;    Grothendieck topologies;    Sheaves;    Gerbes;    Butterflies;   

DOI  :  10.1016/j.jpaa.2019.05.010

来源: Elsevier

【 摘 要 】

Classifying obstructions to the problem of finding extensions between two fixed modules goes back at least to L. Illusie's thesis. Our approach, following in the footsteps of J. Wise, is to introduce an analogous Grothendieck Topology on the category A-mod of modules over a fixed ring A in a topos E. The problem of finding extensions becomes a banded gerbe and furnishes a cohomology class on the site A-mod. We compare our obstruction and that coming from Illusie's work, giving another construction of the exact sequence Illusie used to obtain his obstruction. Our work circumvents the cotangent complex entirely and answers a question posed by Illusie. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free