| Résume | 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 $p$-adic Hodge theory to study this theory of motivic cohomology. |
