Divisibility properties of motivic cohomology, appendix to Motivic periods and Grothendieck arithmetic invariants

Bruno Kahn (1) , F. Andreatta , L. Barbieri-Viale , A. Bertapelle (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 Dipartimento di Matematica [Padova]

We extend results of Colliot-Th\'el\`ene and Raskind on the $\mathcal{K}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences are drawn, such as the degeneration of the Bloch-Lichtenbaum spectral sequence for any field containing $k$.

Domaines: Géométrie algébrique [math.AG]

Bruno Kahn, F. Andreatta, L. Barbieri-Viale, A. Bertapelle. Divisibility properties of motivic cohomology, appendix to Motivic periods and Grothendieck arithmetic invariants. Advances in Mathematics, 2020, 359, pp.106880. ⟨10.1016/j.aim.2019.106880⟩. ⟨hal-02739878⟩