Algebra/Topology seminar by Achim Krause

Abstract:

The world of stable motivic homotopy theory over C looks very similar to classical stable homotopy theory. In particular, one can compare the Adams and Adams-Novikov spectral sequences to learn new things about classical homotopy groups as well.

However, one quickly notices a striking difference: The analogue of the celebrated nilpotence theorems by Nishida and Devinatz-Hopkins-Smith fail in the motivic setting, and in addition to the chromatic v_i, there are more types of self-maps.

In this talk I want to explain our current understanding of this picture, and prove some results towards versions of the periodicity- and thick subcategory theorems that hold in the motivic setting.