Numerically finite hereditary categories with Serre duality
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In this paper, the Grothendieck group modulo the radical of the Euler form is a free abelian group of finite rank with Serre duality, and this condition is satisfied by the category of coherent sheaves on a smooth projective variety.Abstract:
Let 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.read more
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References
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Book
Representation Theory of Artin Algebras
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Triangulated Categories in the Representation of Finite Dimensional Algebras
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TL;DR: In this article, the construction of stable separating tubular families and tubular algebras are discussed. But they do not discuss the relation between tubular extensions and directed algesbras.
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TL;DR: The Bulletin de la S. M. F. as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).