Abstract:

The talk is titled after a paper I wrote with Tony Feng and Allen Yuan. "G" stands for a finite group, "G-spectra" are objects of algebraic topology that resemble representations of a finite group, especially modular representations. "Defects" are invariants of "blocks," not featured in the title but a main subject of the talk. Mainly I will use the talk as an excuse to give an introduction to "Broue's Abelian Defect Conjecture."

Broue's conjecture predicts that a block of Z_p[G] and of Z_p[N] (group rings) have equivalent derived categories, when N is the normalizer of the defect group of the block and this defect group is commutative. In case the defect group is cyclic, there are two old proofs of it, one by Rickard and a while later one by Rouquier. Feng and Yuan and I can construct a similar equivalence between blocks of p-complete G-spectra and p-complete N-spectra, that induces Rouquier's equivalence after taking homology.