EVENT DETAILS AND ABSTRACT

Title: Non-nilpotent elements in motivic homotopy theory
Speaker: Michael Andrews
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Classically, the nilpotence theorem of Devinatz, Hopkins, and Smith tells us that non-nilpotent self maps on finite $p$-local spectra induce nonzero homomorphisms on $BP$-homology. Motivically, this theorem fails to hold: we have a motivic analog of $BP$ and whilst $\eta:S^{1,1}\to S^{0,0}$ induces zero on $BP$-homology, it is non-nilpotent. Recent work with Haynes Miller has led to a computation of $\eta^{-1}\pi_{*,*}(S^{0,0})$; we found it to have a very simple description.

I'll introduce the motivic homotopy category, the motivic Adams SS and the motivic Adams-Novikov SS before describing this theorem. Then I'll talk about future directions and the possibility that there are more periodicity operators in motivic chromatic homotopy theory than in the classical story.