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Classification of abelian hereditary directed categories satisfying Serre duality

Adam-Christiaan van Roosmalen
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Abstract

In an ongoing project to classify all hereditary abelian categories, we provide a classification of 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 the Auslander-Reiten components extensively and use appropriate generalisations of tilting objects and coordinates, namely partial tilting sets and probing of objects by quasi-simples.

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BibTeXRIS

Adam-Christiaan van Roosmalen. 2006-11-09. Classification of abelian hereditary directed categories satisfying Serre duality. https://arxiv.org/abs/math/0601418

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