Special Year Seminar

Motivic Cohomology of Mixed Characteristic Schemes

I will present a new theory of motivic cohomology for general (qcqs) schemes. 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 Dedekind domain after $A^1$-localisation. The construction relies on the syntomic cohomology of Bhatt-Morrow-Scholze and the cdh-local motivic cohomology of Bachmann-Elmanto-Morrow, and generalises the construction of Elmanto-Morrow in the case of schemes over a field.

Date & Time

February 14, 2024 | 2:00pm – 3:00pm


Simonyi 101 and Remote Access


Tess Bouis, Laboratoire de Mathématiques d'Orsay