Title: A higher algebraic approach to liftings of modules over derived quotients Show Chinese title

Title: 一种用于导出商上模的提升的更高代数方法

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. Show Chinese abstract

Abstract: 我们通过高代数的概念，展示了在“导出商”下自$\mathrm{Ext}^2$-消没条件下的模的提升的某种存在性。 这改进了Auslander-Ding-Solberg对完全交的Auslander-Reiten猜想的解法。 结合Auslander的零因子定理，我们证明了在导出商上此类$\mathrm{Ext}$-消没模的存在性等价于局部完全交。