论文标题
半元素Milnor K理论
Semilocal Milnor K-theory
论文作者
论文摘要
在本文中，介绍和研究了半元素米尔诺$ k $ - 田野理论。构建了与半元素Milnor $ k $的强烈收敛频谱序列 - 与半社会动机共同体学理论相关。在重量2中，动机共同体学组$ h^p_ {zar}（k，\ mathbb z（2））$，$ p \ leq 1 $，被计算为半落下的milnor $ k $ k $ - 理论组$ \ wideHat {k}^m_}^m_ {2,3-p}（2,3-p}（k）（k）$。给出了以下申请：（i）Beilinson-Soulé消失的猜想的几个标准； （ii）计算一个字段的$ k_4 $； （iii）Beilinson的理性$ K $ - 主要特征田地理论的猜想表明等于消失的有理半近代的Milnor $ k $ - 理论。
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 $H^p_{Zar}(k,\mathbb Z(2))$, $p\leq 1$, 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.
