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Dimensions of triangulated categories

Published online by Cambridge University Press:  30 November 2007

Raphaël Rouquier
Affiliation:
[email protected] Institut de Mathématiques de Jussieu — CNRS, UFR de Mathématiques, Université Denis Diderot, 2, place Jussieu, 75005 Paris France
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Abstract

We define a dimension for a triangulated category. We prove a representability Theorem for a class of functors on finite dimensional triangulated categories. We study the dimension of the bounded derived category of an algebra or a scheme and we show in particular that the bounded derived category of coherent sheaves over a variety has a finite dimension.

Type
Research Article
Copyright
Copyright © ISOPP 2008

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