© 2000 by London Mathematical Society
© The London Mathematical Society
Splendid Derived Equivalences for Blocks of Finite p-Solvable Groups
School of Mathematics, University of Minnesota 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455-0487, USA
UFR Mathématiques, CNRS, Université Paris VII 2 Place Jussieu, 75251 Parix Cedex 05, France
Received 13 August 1997. Revision received 29 June 1999.
Since the remarkable discovery of the relevance of derived equivalences in the theory of p-blocks of finite groups, where p is a prime, by J. Rickard in [15, 16], various attempts have been made to understand this phenomenon. In particular, J. Rickard defines in [18] a certain class of derived equivalences between the derived module categories of p-blocks of finite groups that he calls splendid equivalences (and that we are going to call splendid derived equivalences in this paper) which take into account the local structure, that is, which under suitable hypotheses induce a family of derived equivalences at all ‘local levels’ of the considered p-blocks (see [18] for a more detailed motivation). The main condition for a derived equivalence to be splendid is that it is given by a two-sided tilting complex consisting of p-permutation bimodules (see Definitions 1.3 and 1.4 below for the precise terminology).