Numerically finite hereditary categories with Serre duality
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- by Adam-Christiaan van Roosmalen PDF
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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.References
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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
- Received by editor(s): April 21, 2014
- Received by editor(s) in revised form: September 11, 2014
- Published electronically: February 11, 2016
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3471089