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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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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
Published electronically: January 18, 2002


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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Bibliographic Information
  • I. Reiten
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
  • Email:
  • M. Van den Bergh
  • Affiliation: Department WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium
  • MR Author ID: 176980
  • Email:
  • Received by editor(s): December 6, 2000
  • Published electronically: January 18, 2002
  • Additional Notes: The second author is a senior researcher at the Fund for Scientific Research. The second author also wishes to thank the Clay Mathematics Institute for material support during the period in which this paper was written.
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 15 (2002), 295-366
  • MSC (2000): Primary 18E10, 18G20, 16G10, 16G20, 16G30, 16G70
  • DOI:
  • MathSciNet review: 1887637