2 00 1 Noetherian hereditary abelian categories satisfying Serre duality
نویسندگان
چکیده
In this paper we classify 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 nonzero projectives or injectives, then the Serre duality property is equivalent to the existence of almost split sequences.
منابع مشابه
Noetherian Hereditary Abelian Categories Satisfying Serre Duality
Notations and conventions 296 Introduction 296 I. Serre duality and almost split sequences 300 I.1. Preliminaries on Serre duality 300 I.2. Connection between Serre duality and Auslander–Reiten triangles 304 I.3. Serre functors on hereditary abelian categories 307 II. Hereditary noetherian abelian categories with non-zero projective objects 309 II.1. Hereditary abelian categories constructed fr...
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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 ...
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