Motivic cohomology of singular schemesMPIM

by Tess Bouis (Universität Regensburg)

Friday Dec 13, 2024, 2:05 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

https://www.mpim-bonn.mpg.de/node/13773

I will present a new theory of motivic cohomology for general (qcqs) schemes, which generalises the construction of Elmanto-Morrow over a field. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A^1-invariant in general, but it recovers classical motivic cohomology on smooth schemes over a field (by the work of Elmanto-Morrow) or over a Dedekind domain (by recent work in progress with Arnab Kundu). I will also discuss how one can import results from prismatic cohomology to study this theory of motivic cohomology.