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arXiv · 2503.17964

A higher algebraic approach to liftings of modules over derived quotients

Ryo Ishizuka
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Abstract

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.

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Ryo Ishizuka. 2025-03-23. A higher algebraic approach to liftings of modules over derived quotients. https://arxiv.org/abs/2503.17964

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