Noetherian hereditary categories satisfying Serre duality
Representation Theory
2007-05-23 v2 Category Theory
Abstract
In this paper we classify noetherian hereditary abelian categories satisfying Serre duality in the sense of Bondal and Kapranov. As a consequence we obtain a classification of saturated noetherian hereditary categories. As a side result we show that when our hereditary categories have no nonzero projectives or injectives, then the Serre duality property is equivalent to the existence of almost split sequences.
Cite
@article{arxiv.math/9911242,
title = {Noetherian hereditary categories satisfying Serre duality},
author = {Idun Reiten and Michel Van den Bergh},
journal= {arXiv preprint arXiv:math/9911242},
year = {2007}
}
Comments
Final version; minor changes