Divisibility properties of motivic cohomology

Abstract

We extend results of Colliot-Thélène and Raskind on the ${\mathcal{K}}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the étale 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 $k$.

8 pages

References in corpus (5)

• 1-motivic sheaves and the Albanese functor
• Sharp de Rham realization
• On descending cohomology geometrically
• Ogus realization of 1-motives
• The Brauer group and indecomposable (2,1)-cycles

Cited by in corpus (2)

• Mixed Motives
• On Suslin homology with integral coefficients in characteristic zero (with an appendix by Bruno Kahn)