Motivic homotopy theory of logarithmic schemes

by Doosung Park (Universität Zürich)

Thursday 8 Apr 2021, 12:30 → 14:30 Europe/Moscow

818-1526-4739 (Zoom)

Morel and Voevodsky constructed the $\mathbb{A}^1$-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 $\mathbb{A}^1$-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.

Video