Noetherian hereditary abelian categories satisfying Serre duality

Reiten, I.; Van den Bergh, M.

doi:10.1090/S0894-0347-02-00387-9

Noetherian hereditary abelian categories satisfying Serre duality
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by I. Reiten and M. Van den Bergh

J. Amer. Math. Soc. 15 (2002), 295-366

DOI: https://doi.org/10.1090/S0894-0347-02-00387-9

Published electronically: January 18, 2002

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Abstract:

In this paper we classify $\operatorname {Ext}$-finite noetherian hereditary abelian categories over an algebraically closed field $k$ satisfying Serre duality in the sense of Bondal and Kapranov. As a consequence we obtain a classification of saturated noetherian hereditary abelian categories. As a side result we show that when our hereditary abelian categories have no non-zero projectives or injectives, then the Serre duality property is equivalent to the existence of almost split sequences.

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