A characterization of the hereditary categories derived equivalent to some category of coherent sheaves on a weighted projective line
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- by Dieter Happel and Idun Reiten PDF
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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 $\operatorname {coh}\mathbb {X}$ 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.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 643-651
- MSC (1991): Primary 16B50, 16E10, 16G70, 18E10, 18E30
- DOI: https://doi.org/10.1090/S0002-9939-01-06159-7
- MathSciNet review: 1866014