A higher algebraic approach to liftings of modules over derived quotients

Fuente: arXiv
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Main Author: Ishizuka, Ryo
Format: Preprint
Published: 2025
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author Ishizuka, Ryo
author_facet Ishizuka, Ryo
contents We show a certain existence of a lifting of modules under the self-$\mathrm{Ext}^2$-vanishing condition over the "derived quotient" by using the notion of higher algebra. This refines a work of Auslander-Ding-Solberg's solution of the Auslander-Reiten conjecture for complete interesctions. Together with Auslander's zero-divisor theorem, we show that the existence of such $\mathrm{Ext}$-vanishing module over derived quotients is equivalent to being local complete intersections.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17964
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A higher algebraic approach to liftings of modules over derived quotients
Ishizuka, Ryo
Commutative Algebra
Number Theory
Rings and Algebras
We show a certain existence of a lifting of modules under the self-$\mathrm{Ext}^2$-vanishing condition over the "derived quotient" by using the notion of higher algebra. This refines a work of Auslander-Ding-Solberg's solution of the Auslander-Reiten conjecture for complete interesctions. Together with Auslander's zero-divisor theorem, we show that the existence of such $\mathrm{Ext}$-vanishing module over derived quotients is equivalent to being local complete intersections.
title A higher algebraic approach to liftings of modules over derived quotients
topic Commutative Algebra
Number Theory
Rings and Algebras
url https://arxiv.org/abs/2503.17964