Homotopy Theory Seminar
Friday, March 18, 2022 - 2:00pm
Paul VanKoughnett
Texas A&M University
Certain p-adic Lie groups have the property that their cohomology admits a finite-length resolutions in terms of the cohomology of their finite subgroups. This phenomenon was first observed in stable homotopy theory by Goerss-Henn-Mahowald-Rezk, who used such a resolution of the height 2 Morava stabilizer group at the prime 3 to construct a topological resolution for the K(2)-local sphere. I'll describe a new resolution for the analogous case of the group SL_2(Z_3), as well as some attempts to construct such resolutions for general p-adic Lie groups. This is joint work with Eva Belmont and Catherine Ray.