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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of the hereditary categories derived equivalent to some category of coherent sheaves on a weighted projective line


Authors: Dieter Happel and Idun Reiten
Journal: Proc. Amer. Math. Soc. 130 (2002), 643-651
MSC (1991): Primary 16B50, 16E10, 16G70, 18E10, 18E30
Published electronically: September 28, 2001
MathSciNet review: 1866014
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Abstract: Let $\mathcal{H}$ be a connected hereditary abelian category over an algebraically closed field $k$, with finite dimensional homomorphism and extension spaces. There are two main known types of such categories: those derived equivalent to $\operatorname{mod}\lambda$ for some finite dimensional hereditary $k$-algebra $\lambda$ and those derived equivalent to some category $\mathrm{coh}\,\mathbb{X} $ of coherent sheaves on a weighted projective line $\mathbb{X} $ in the sense of Geigle and Lenzing (1987). The aim of this paper is to give a characterization of the second class in terms of some properties known to hold for these hereditary categories.


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Additional Information

Dieter Happel
Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Email: happel@mathematik.tu-chemnitz.de

Idun Reiten
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: idunr@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06159-7
PII: S 0002-9939(01)06159-7
Received by editor(s): January 13, 2000
Received by editor(s) in revised form: September 12, 2000
Published electronically: September 28, 2001
Communicated by: Ken Goodearl
Article copyright: © Copyright 2001 American Mathematical Society