We solve two open problems: first we prove a conjecture of Bondal and Van den Bergh,
showing that the category D^perf(X) is strongly generated whenever X is a quasicompact …

This work is concerned with both strong generation and (co) ghost index in the module
category of a commutative noetherian ring. A sufficiency criterion is established for such …

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …

We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

The cohomology annihilator of a noetherian ring that is finitely generated as a module over
its center is introduced. Results are established linking the existence of nontrivial …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …

We classify certain resolving subcategories of finitely generated modules over a
commutative noetherian ring R by using integer-valued functions on SpecR. As an …

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 …

Several years ago, Bondal, Rouquier, and Van den Bergh introduced the notion of the
dimension of a triangulated category, and Rouquier proved that the bounded derived …

Let AA be an abelian category having enough projective objects and enough injective
objects. We prove that if AA admits an additive generating object, then the extension …