2020
DOI: 10.1016/j.jpaa.2019.05.010
|View full text |Cite
|
Sign up to set email alerts
|

Deformations of modules through butterflies and gerbes

Abstract: 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… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

0
4
0

Year Published

2022
2022
2022
2022

Publication Types

Select...
1

Relationship

1
0

Authors

Journals

citations
Cited by 1 publication
(4 citation statements)
references
References 5 publications
0
4
0
Order By: Relevance
“…• obtains the theorems of [Her20] about modules for algebras, • fixes a subtle flaw (Example A.3) in [Wis12]. This class vanishes if and only if there is a solution B ′ to Question 0.1.…”
Section: This Papermentioning
confidence: 97%
See 3 more Smart Citations
“…• obtains the theorems of [Her20] about modules for algebras, • fixes a subtle flaw (Example A.3) in [Wis12]. This class vanishes if and only if there is a solution B ′ to Question 0.1.…”
Section: This Papermentioning
confidence: 97%
“…Remark 3.4. One can obtain the same map Hom A (I, M ) → Exal 2 A (B, M ) as in [Her20,§4]. Choose a flat A ′ -algebra with a surjection P → B:…”
Section: Deformations Fix the Extension Of Algebras (8)mentioning
confidence: 97%
See 2 more Smart Citations