A higher algebraic approach to liftings of modules over derived quotients

We show a certain existence of a lifting of modules under the self-${\mathrm{E}\mathrm{x}\mathrm{t}}^2$-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 $\mathrm{E}\mathrm{x}\mathrm{t}$-vanishing module over derived quotients is equivalent to being local complete intersections.