Hermitian $K$-theory, Dedekind $\zeta$-functions, and quadratic forms over rings of integers in number fields

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-11-09 DOI:10.4310/cjm.2020.v8.n3.a3

Jonas Irgens Kylling, O. Rondigs, P. Ostvaer

引用次数: 9

Abstract

We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian $K$-groups of rings of integers in number fields. Moreover, we relate the orders of these groups to special values of Dedekind $\zeta$-functions for totally real abelian number fields. Our methods apply more readily to the examples of algebraic $K$-theory and higher Witt-theory, and give a complete set of invariants for quadratic forms over rings of integers in number fields.

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Hermitian$K$理论、Dedekind$\zeta$函数和数域中整数环上的二次形式

我们利用切片谱序列、动机Steenrod代数和Voevodsky的Milnor猜想和Bloch-Kato猜想的解来计算数域中整数环的埃尔米特K群。此外，我们将这些群的阶数与完全实数域的Dedekind $\zeta$-函数的特殊值联系起来。我们的方法更易于应用于代数K理论和高等witt理论的例子，并给出了整数环上二次型在数域上的不变量的完整集合。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.