Morita equivalence classes of $2$-blocks with abelian defect groups of rank $4$ (2310.05734v3)

Abstract: We classify all $2$-blocks with abelian defect groups of rank $4$ up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application is that Brou\'{e}'s abelian defect group conjecture holds for all blocks under consideration here.