Raphael Rouquier
Institut de Mathematiques de Jussieu and Universite Paris 7


We define a dimension for a triangulated category. We prove a representability
Theorem for a certain 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.
For a self-injective algebra, a lower bound for Auslander's representation
dimension is given by the dimension of the stable category. We use this
to compute the representation dimension of exterior algebras. This
provides the first known examples of representation dimension >3. We
deduce that the Loewy length of the group algebra over F_2 of a finite group
is strictly bounded below by 2-rank of the group (a conjecture of Benson).