We establish a general method to construct triangle equivalences between the singularity
categories of (commutative and non-commutative) Gorenstein rings and the cluster …

Given a negatively graded Calabi-Yau algebra, we regard it as a DG algebra with vanishing
differentials and study its cluster category. We show that this DG algebra is sign-twisted …

For an exact category EE with enough projectives and with ad Z d Z-cluster tilting
subcategory, we show that the singularity category of EE admits ad Z d Z-cluster tilting …

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 …

Auslander-Reiten duality for module categories is generalized to some sufficiently nice
subcategories. In particular, our consideration works for $\mathcal {P}^{<\infty}(\Lambda) …

Proceedings of the International Congress of Mathematicians (ICM 2018) : TILTING COHEN–MACAULAY
REPRESENTATIONS Page 1 P . I . C . M . – 2018 Rio de Janeiro, Vol. 2 (125–162) TILTING …

We investigate (existence of) Auslander–Reiten triangles in a triangulated category in
connection with torsion pairs, existence of Serre functors, representability of homological …

Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization …

We study homological properties of contravariantly finite rigid subcategories of an arbitrary
triangulated or abelian category, concentrating at the class of higher cluster tilting …

We prove that a certain eventually homological isomorphism between module categories
induces triangle equivalences between their singularity categories, Gorenstein defect …