Semilocal Milnor K-Theory
Semilocal Milnor K-Theory
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半局部米尔诺K理论
DOI：
10.1093/imrn/rnac343
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发表时间：
2022
影响因子：
1
通讯作者：
Garkusha G
中科院分区：
文献类型：
--
作者：
Garkusha G
本文介绍并研究了半局部Milno场论。构造了一个将半局部Milnor-theory与半局部motivic上同调联系起来的强收敛谱序列。在权2中，动机上同调群被计算为半局部Milnor-theory群。给出了下列应用：（i）Beilinson-Soulé消失猜想的几个判据;（ii）域的计算;（iii）素特征域的有理理论的Beilinson猜想等价于有理半局部Milnor-theory的消失.
In this paper, semilocal Milnor-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology groups,, are computed as semilocal Milnor-theory groups. The following applications are given: (i) several criteria for the Beilinson–Soulé Vanishing Conjecture; (ii) computation ofof a field; (iii) the Beilinson conjecture for rational-theory of fields of prime characteristic is shown to be equivalent to vanishing of rational semilocal Milnor-theory.