Noetherian hereditary abelian categories satisfying Serre duality

Reiten, I.; Van den Bergh, M.

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

¹Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
²Department WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium

Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 295-366

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Résumé

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.

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

Affiliations des auteurs :

Reiten, I. ¹ ; Van den Bergh, M. ²

¹ Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
² Department WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium

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Reiten, I.; Van den Bergh, M. Noetherian hereditary abelian categories satisfying Serre duality. Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 295-366. doi: 10.1090/S0894-0347-02-00387-9

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