Alvis-Curtis Duality as an Equivalence of Derived Categories

by Marc Cabanes, Université Paris 7 
and Jeremy Rickard, University of Bristol 

Let G be the group of rational points of a connected reductive
group defined over a finite field of characteristic p, and let
O be any commutative ring in which p is invertible. We prove
that the duality operation of Alvis, Curtis, Kawanaka and Lusztig on
the characters of G is induced by a self-equivalence of the
derived category of OG-modules, which was conjectured by
Broué. We also prove that this equivalence of derived categories
is compatible with Harish-Chandra induction and truncation.