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Noetherian hereditary abelian categories satisfying Serre duality
- Source :
- Journal of the American Mathematical Society; 2002, Vol. 15 Issue: 2 p295-366, 72p
- Publication Year :
- 2002
-
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.
Details
- Language :
- English
- ISSN :
- 08940347 and 10886834
- Volume :
- 15
- Issue :
- 2
- Database :
- Supplemental Index
- Journal :
- Journal of the American Mathematical Society
- Publication Type :
- Periodical
- Accession number :
- ejs1987748