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Hermitian $K$-theory, Dedekind $\zeta$-functions, and quadratic forms over rings of integers in number fields
Cambridge Journal of Mathematics ( IF 1.8 ) Pub Date : 2020-10-02 , DOI: 10.4310/cjm.2020.v8.n3.a3
Jonas Irgens Kylling 1 , Röndigs Oliver 2 , Paul Arne Østvær 1
Affiliation  

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.

中文翻译:

Hermitian $ K $-理论,Dedekind $ \ zeta $-函数以及数字字段中的整数环的二次形式

我们使用切片频谱序列,动机Steenrod代数以及Milnor和Bloch-Kato猜想的Voevodsky解,来计算数字字段中整数环的埃尔米特$ K $-组。此外,我们将这些组的顺序与Dedekind $ \ zeta $函数的特殊值相关联,以表示完全真实的阿贝尔数字段。我们的方法更容易应用于代数$ K $-理论和更高的Witt-理论的示例,并给出了整数形式的整数形式的完整不变量集,这些变量在数字字段中的整数环上。
更新日期:2020-10-02
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