Classification of abelian hereditary directed categories satisfying Serre duality

van Roosmalen, Adam-Christiaan

doi:10.1090/S0002-9947-07-04426-1

Classification of abelian hereditary directed categories satisfying Serre duality
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by Adam-Christiaan van Roosmalen PDF

Trans. Amer. Math. Soc. 360 (2008), 2467-2503 Request permission

Abstract:

In an ongoing project to classify all hereditary abelian categories, we provide a classification of $\operatorname {Ext}$-finite directed hereditary abelian categories satisfying Serre duality up to derived equivalence. In order to prove the classification, we will study the shapes of Auslander-Reiten components extensively and use appropriate generalizations of tilting objects and coordinates, namely partial tilting sets and probing of objects by quasi-simples.

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