Algebraic Topology Seminar
Monday, October 21, 2019 at 4:30pm
Room : 2 - 131 182 memorial Drive, MIT Building 2, Cambridge, MA, 02142
The motivic kq-resolution
(Joint work with Dominic Culver) Let kq denote the very effective cover of Hermitian K- theory. The kq-based motivic Adams spectral sequence, or kq-resolution, is a motivic analog of Mahowalds bo-resolution. We applied the kq-resolution in the C-motivic setting to calculate the η-periodic stable stems (recovering results of Andrews, Guillou, Isaksen, and Miller) and v1-periodic stable stems. I will summarize these calculations and discuss work in progress towards analogous results over general base fields and in the C2-equivariant setting. In addition to large-scale calculations of periodic phenomena, the kq-resolution can be used to calculate low-dimensional 2-complete Milnor-Witt stems. I will present some calculations in the C- and R-motivic settings (recovering results of Dugger-Isaksen), then discuss work in progress towards analogous results over general base fields and the 2-complete version of calculations of Rndigs-Spitzweck- Østvaer.
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