Doosung Park | Motivic homotopy theory of logarithmic schemes

Seminar on A1-topology, motives and K-theory, April 8, 2021
Doosung Park (Universität Zürich)
Motivic homotopy theory of logarithmic schemes

Morel and Voevodsky constructed the A1-motivic homotopy category SH(k). One purpose of motivic homotopy theory is to incorporate various cohomology theories into a single framework so that one can discuss relations between cohomology theories more efficiently. However, there are still lots of non A1-invariant cohomology theories, e.g. Hodge cohomology and topological cyclic homology. There is no way to represent these in SH(k). In this talk, I will explain the construction of the logarithmic motivic homotopy category logSH(k) and how we can represent TC in logSH(k).

This work is joint with Federico Binda and Paul Arne Østvær.