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

IF 1.8 2区 数学 Q1 MATHEMATICS
Jonas Irgens Kylling, O. Rondigs, P. Ostvaer
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引用次数: 9

摘要

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。
Hermitian $K$-theory, Dedekind $\zeta$-functions, and quadratic forms over rings of integers in number fields
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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CiteScore
3.10
自引率
0.00%
发文量
7
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