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Numerically finite hereditary categories with Serre duality


Author: Adam-Christiaan van Roosmalen
Journal: Trans. Amer. Math. Soc. 368 (2016), 7189-7238
MSC (2010): Primary 18E10, 18E30, 18G20; Secondary 16G20, 14F05
DOI: https://doi.org/10.1090/tran/6569
Published electronically: February 11, 2016
MathSciNet review: 3471089
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Abstract: Let $ \mathcal {A}$ be an abelian hereditary category with Serre duality. We provide a classification of such categories up to derived equivalence under the additional condition that the Grothendieck group modulo the radical of the Euler form is a free abelian group of finite rank. Such categories are called numerically finite and this condition is satisfied by the category of coherent sheaves on a smooth projective variety.


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Additional Information

Adam-Christiaan van Roosmalen
Affiliation: Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Address at time of publication: Department of Mathematics and Statistics, Hasselt University, B-3590 Diepenbeek, Belgium
Email: vanroosmalen@karlin.mff.cuni.cz, adamchristiaan.vanroosmalen@uhasselt.be

DOI: https://doi.org/10.1090/tran/6569
Received by editor(s): April 21, 2014
Received by editor(s) in revised form: September 11, 2014
Published electronically: February 11, 2016
Article copyright: © Copyright 2016 American Mathematical Society