Morita equivalence classes of $2$-blocks of defect three

Abstract

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order $8$ and of the derived equivalences between them. A consequence is the verification of Brou\'e's abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of $2$-blocks of defect at most three defined over a suitable field.