David Treumann (Boston College)

Broue’s Abelian Defect Conjecture concerns the derived categories of representations of finite groups in characteristic p. It says that the derived category of F_q[G] and the derived category of F_q[N_G(D)] have direct factors in common so long as (1) D is abelian of p-power order and (2) D is the defect group of one of the blocks of G. Tony Feng and Allen Yuan and I have investigated a version of this conjecture in algebraic topology: do the categories of p-complete G-spectra and p-complete N_G(D)-spectra have direct factors in common? We can prove it when D is a cyclic group.