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- W4309793887 abstract "In this paper, semilocal Milnor $K$-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor $K$-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology groups $H^p_{Zar}(k,mathbb Z(2))$, $pleq 1$, 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-Soul'e 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." @default.
- W4309793887 created "2022-11-29" @default.
- W4309793887 creator A5086130780 @default.
- W4309793887 date "2020-07-17" @default.
- W4309793887 modified "2023-09-23" @default.
- W4309793887 title "Semilocal Milnor K-theory" @default.
- W4309793887 doi "https://doi.org/10.48550/arxiv.2007.09044" @default.
- W4309793887 hasPublicationYear "2020" @default.
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