Wild kernels and divisibility in K-groups of global fields

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• 作者：Grzegorz Banaszak
• 关键词：19D10 ; 11G30
• 刊名：Journal of Number Theory
• 出版年：2013
• 出版时间：October, 2013
• 年：2013
• 卷：133
• 期：10
• 页码：3207-3244
• 全文大小：537 K

文摘

Text

In this paper we study divisibility and 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 the Quillen-Lichtenbaum conjecture for F is equivalent to the equality of wild kernels with the 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 ¨¦tale divisible elements and we apply this result for the proof of the analogue of the 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 . 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 the corresponding groups of divisible elements.

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