Brou\'e's abelian defect group conjecture for the Held group 
and the sporadic Suzuki group
Shigeo Koshitani, Naoko Kunugi and Katsushi Waki

Abstract.
In the representation theory of finite groups, there is a 
well known and important conjecture due to M. Brou\'e. He
conjectures that, for any prime p, if a p-block A of a 
finite group G has an abelian defect group P, then A and
its Brauer corresponding p-block B of N_G(P) are derived
equivalent. We demonstrate in this paper that Brou\'e's
conjecture holds for non-principal 3-blocks A with
elementary abelain defect group P of order 9 of the simple
Held group and the sporadic simple Suzuki group.