We study the category of matrix factorizations associated to the germ of an isolated
hypersurface singularity. This category is shown to admit a compact generator which is …

In a recent paper, Iyama and Yoshino considered two interesting examples of isolated
singularities over which it is possible to classify the indecomposable maximal Cohen …

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-
separated noetherian scheme, and study these complexes using the pure derived category …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a …

For a Frobenius abelian category $\mathcal {A} $, we show that the category ${\rm
Mon}(\mathcal {A}) $ of monomorphisms in $\mathcal {A} $ is a Frobenius exact category; …

The Gorenstein derived category is introduced and studied via Verdier's localization of
homotopy category respect to the saturated multiplicative system of Gorenstein quasi …

We prove that if a positively-graded ring $ R $ is Gorenstein and the associated torsion
functor has finite cohomological dimension, then the corresponding noncommutative …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely-generated Gorenstein-projective A-modules. We prove that for a …