范簇和链引理（在Markus Rost之后）
Norm Varieties and the Chain Lemma (after Markus Rost)
摘要：
本文的目的是证明Markus Rost的两个结果：链引理和范数原理。这些是完成Bloch-Kato猜想的可验证性所需的最后步骤，即对于每个素数p，每个n和每个包含1/p的域k，范剩余映射是Milnor K-理论$K_n^M(k)/p$和etale上同调$H^n(k,μ_p^n)$之间的同构。我们对这两个结果的证明基于Rost的1998年预印本，他的网站和罗斯特在1999-2000年和2005年在高等研究院的讲座。
英文摘要：
The goal of this paper is to present proofs of two results of Markus Rost: the Chain Lemma and the Norm Principle. These are the final steps needed to complete the publishable verification of the Bloch-Kato conjecture, that the norm residue maps are isomorphisms between Milnor K-theory $K_n^M(k)/p$ and etale cohomology $H^n(k,μ_p^n)$ for every prime p, every n and every field k containing 1/p. Our proofs of these two results are based on Rost's 1998 preprints, his web site and Rost's lectures at the Institute for Advanced Study in 1999-2000 and 2005.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
