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Noetherian hereditary categories satisfying Serre duality

Idun Reiten·Michel Van den Bergh
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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.

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Idun Reiten, Michel Van den Bergh. 2001-12-04. Noetherian hereditary categories satisfying Serre duality. https://arxiv.org/abs/math/9911242

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