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Dimensions of triangulated categories

Published online by Cambridge University Press:  30 November 2007

Raphaël Rouquier
Raphaël Rouquier
Affiliation:
rouquier@math.jussieu.fr 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.

Keywords

homological algebraderived categoriestriangulated categoriesdimensionsBrown representability
Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 2 , April 2008 , pp. 193 - 256
Copyright
Copyright © ISOPP 2008

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