霜冻品种的存在

The Norm Residue Theorem in Motivic Cohomology Pub Date : 2019-06-11 DOI:10.2307/j.ctv941tx2.16

C. Haesemeyer, C. Weibel

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摘要

本章证明了前一章构建的范数品种确实是罗斯特品种。换句话说，它证明了Rost品种的存在。在这样做的过程中，本章也证明了范数原理，这是一个假设𝑘是特征为0的𝓁-special域，并且𝑋是一些非平凡符号ª的范数变化的定理。那么，每个元素(𝐻−1，−1(𝑋))都是一个Kummer元素。为了准备范数原理的证明，本章发展了一些基本事实，这些基本事实是关于在点上以𝑘(s1):𝑘=𝓁支持的ω𝐻−1，ω 1(𝑋)的元素。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence of Rost Varieties

This chapter proves that the norm varieties constructed in the previous chapter are indeed Rost varieties. In other words, it proves that Rost varieties exist. In doing so, the chapter also proves the Norm Principle, which is a theorem that supposes that 𝑘 is an 𝓁-special field of characteristic 0, and that 𝑋 is a norm variety for some nontrivial symbol ª. Then each element of ̅𝐻−1, −1(𝑋) is a Kummer element. In preparation for the proof of the Norm Principle, this chapter develops some basic facts about elements of ̅𝐻−1, −1(𝑋) supported on points 𝑥 with 𝑘(𝑥) : 𝑘=𝓁.

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The Norm Residue Theorem in Motivic Cohomology

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