Towards integral equivariant rigidity

Speaker: Irakli Patchkoria

Speaker organization: University of Copenhagen

Abstract: Let p be an odd prime and G a finite group such that p does not divide the order of G. We show that the p-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. The proof is a generalization of Schwede's proof in the nonequivariant case and uses that the group algebra F_p[G x G] is semisimple. Combining this with our previous result about the 2-local G-equivariant stable homotopy category, we get an integral equivariant rigidity theorem for any finite 2-group.