1. INTRODUCTION wx In this note we aim to complete some of the results in 8, 9, 14, 13. In
these papers the authors are concerned with local cohomology, Serre duality, and dualizing …

" Ha habido muy pocas exposiciones sistemáticas de la teoría de las categorías derivadas
desde su inicio en el trabajo de Grothendieck y Verdier en la década de 1960. Este libro es …

A ring with an Auslander dualizing complex is a generalization of an Auslander–Gorenstein
ring. We show that many results which hold for Auslander–Gorenstein rings also hold in the …

If we were very clever, we might be able to solve the following problem: Let A be a
noetherian N-graded connected k-algebra given by generators and relations. Now …

In establishing a more general version of the McKay correspondence, we prove Auslander's
theorem for actions of semisimple Hopf algebras H on noncommutative Artin–Schelter …

In this paper, we define a notion of noncommutative graded isolated singularity, and study
AS-Gorenstein isolated singularities and the categories of graded maximal Cohen …

We continue our study of the McKay Correspondence for grading preserving actions of
semisimple Hopf algebras H on (noncommutative) Artin–Schelter regular algebras A. Here …

Let k be a field and A be a noetherian graded algebra finitely generated in degree 1 over k.
There are two basic ingredients to study A in noncommutative algebraic geometry, namely …

Classification of AS-regular algebras is one of the major projects in non-commutative
algebraic geometry. In this paper, we will study when given AS-regular algebras are graded …

We prove an existence theorem for dualizing complexes over noncommutative noetherian
complete semilocal algebras, which generalizes Van den Bergh's existence theorem in the …