Semilocal Milnor K-theory

by Grigory Garkusha (Swansea University)

Thursday 22 Oct 2020, 12:30 → 14:30 Europe/Moscow

958-115-833 (Zoom)

In this talk I will tell about semilocal Milnor $K$-theory of fields. A strongly convergent spectral sequence relating semilocal Milnor $K$-theory to semilocal motivic cohomology is constructed. In weight $2$, the motivic cohomology groups $H^p_{Zar}(k,\mathbb Z(2))$, $p\le 1$, are computed as semilocal Milnor $K$-theory groups $\widehat{K}^M_{2,3-p}(k)$. The following applications are given: (i) several criteria for the Beilinson-Soulé Vanishing Conjecture; (ii) computation of $K_4$ of a field; (iii) the Beilinson conjecture for rational $K$-theory of fields of prime characteristic is shown to be equivalent to vanishing of rational semilocal Milnor $K$-theory.

Notes from the talk Video