Abstract:
I will speak about the paper https://arxiv.org/abs/2207.13408 by Håkon Schad Bergsaker and myself (J. of Topology, 2023), comparing G-fixed points and G-homotopy fixed points for G-fold smash products of bounded below spectra of finite type, concentrating on the case where G is a finite p-group. The result specializes to Segal's original Burnside ring conjecture in the case of the sphere spectrum, as proven in the early 1980s by Gunnar Carlsson and others.