整体域K-群的Wild核与整除性
Wild Kernels and divisibility in K-groups of global fields
摘要：
本文研究了整体域$F.$的代数K理论中的可除性和野核，将野核的概念推广到整体域的所有K-群，证明了对$F$的Quillen-Lichtenbaum猜想等价于野核与$F.$的K-群中相应的可除元素群相等，并证明了对偶数K-群存在广义Moore正合列。全局字段组。在不诉诸Quillen-Lichtenbaum猜想的情况下，我们证明了可分元素群与相应的\' etale可分元素群同构，并将此结果应用于Quillen-Lichtenbaum猜想的$lim^1$类似物的证明.我们也应用这个同构来研究：$GL,$同调中的嵌入障碍Quillen局部化序列的分裂障碍可除元素群通过$ζ_{F}(s).$的特殊值的阶利用Bloch，Friedlander，Levine，Lichtenbaum，Morel，Rost，Suslin，Voevodsky和Weibel的motivic上同调结果建立了Quillen-Lichtenbaum猜想，我们的结论是，野生核等于相应的可分元素组
英文摘要：
In this paper we study the divisibility and the wild kernels in algebraic K-theory of global fields $F.$ We extend the notion of the wild kernel to all K-groups of global fields and prove that Quillen-Lichtenbaum conjecture for $F$ is equivalent to the equality of wild kernels with corresponding groups of divisible elements in K-groups of $F.$ We show that there exist generalized Moore exact sequences for even K-groups of global fields. Without appealing to the Quillen-Lichtenbaum conjecture we show that the group of divisible elements is isomorphic to the corresponding group of \' etale divisible elements and we apply this result for the proof of the $lim^1$ analogue of Quillen-Lichtenbaum conjecture. We also apply this isomorphism to investigate: the imbedding obstructions in homology of $GL,$ the splitting obstructions for the Quillen localization sequence, the order of the group of divisible elements via special values of $ζ_{F}(s).$ Using the motivic cohomology results due to Bloch, Friedlander, Levine, Lichtenbaum, Morel, Rost, Suslin, Voevodsky and Weibel, which established the Quillen-Lichtenbaum conjecture, we conclude that wild kernels are equal to corresponding groups of divisible elements
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