Let $ R $ be a Cohen-Macaulay ring and $ M $ a maximal Cohen-Macaulay $ R $-module.
Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and van den Bergh …

We classify all tilting and cotilting classes over commutative noetherian rings in terms of
descending sequences of specialization closed subsets of the Zariski spectrum …

We prove that in a 2-Calabi–Yau triangulated category, each cluster tilting subcategory is
Gorenstein with all its finitely generated projectives of injective dimension at most one. We …

We shall show that the stable categories of graded Cohen–Macaulay modules over quotient
singularities have tilting objects. In particular, these categories are triangle equivalent to …

In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main
result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen …

We study Artin algebras Λ and commutative Noetherian complete local rings R in connection
with the following decomposition property of Gorenstein-projective modules: We show that …

Let R be a commutative noetherian local ring. As an analog of the notion of the dimension of
a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of …

We prove two theorems on the vanishing of Ext over commutative Noetherian local rings.
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …

We introduce a new invariant for subcategories X of finitely generated modules over a local
ring R which we call the radius of X. We show that if R is a complete intersection and X is …