论文标题
Borel的Artin $ L $ functions的排名定理
Borel's rank theorem for Artin $L$-functions
论文作者
论文摘要
Borel的排名定理标识了数字字段整数环的代数$ k $ - 组的等级，并在该字段上附加了Dedekind Zeta函数的命令。在GROSS的工作之后，我们通过考虑具有等效的代数$ K $ - 数字字段的等效代数$ k $ groups，为具有理性galois表示的系数建立了该定理的版本。该结构涉及与理性摩尔光谱的代数$ k $ - 理论光谱。我们进一步讨论了与Galois表示相关的整体摩尔光谱及其在$ l $ functions中的潜在应用。
Borel's rank theorem identifies the ranks of algebraic $K$-groups of the ring of integers of a number field with the orders of vanishing of the Dedekind zeta function attached to the field. Following the work of Gross, we establish a version of this theorem for Artin $L$-functions by considering equivariant algebraic $K$-groups of number fields with coefficients in rational Galois representations. This construction involves twisting algebraic $K$-theory spectra with rational equivariant Moore spectra. We further discuss integral equivariant Moore spectra attached to Galois representations and their potential applications in $L$-functions.
