A differential graded approach to the silting theorem

A silting theorem was established by Buan and Zhou as a generalisation of the classical tilting theorem of Brenner and Butler. In this paper, we give an alternative proof of the theorem by using differential graded algebras.

A Bijection theorem for Gorenstein projective tau-tilting modules

In this paper, we introduce the notions of Gorenstein projective $tau$-rigid modules, Gorenstein projective support $tau$-tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi-Iyama-Reitens bijection theorem on support $tau$-tilting modules. More precisely, for an algebra $Lambda$, we show that there is a bijection between the set of Gorenstein projective $tau$-rigid pairs in $mod Lambda$ and the set of Gorenstein injective $tau^{-1}$-rigid pairs in $mod Lambda^{rm op}$. We prove that there is a bijection between the set of Gorenstein projective support $tau$-tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM-$tau$-tilting finite algebras and show that $Lambda$ is CM-$tau$-tilting finite if and only if $Lambda^{rm {op}}$ is CM-$tau$-tilting finite.