$L$-functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups

Canadian mathematical bulletin

Jonathan W. Sands¹ 

[1] Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA

关键词: motivic cohomology;    regulator;    Artin L-functions;   

DOI  :  10.4153/CMB-2014-072-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $n$ be a positive even integer, and let $F$ be a totally realnumber field and $L$ be an abelian Galois extension which is totallyreal or CM. Fix a finite set $S$ of primes of $F$ containing the infinite primesand all those which ramify in $L$, and let $S_L$ denote the primes of $L$ lying above those in$S$. Then $mathcal{O}_L^S$ denotes the ring of $S_L$-integers of $L$.Suppose that $psi$ is a quadratic character of the Galois group of$L$ over $F$. Under the assumption of the motivic Lichtenbaumconjecture, we obtain a non-trivial annihilator of the motiviccohomology group $H_mathcal{M}^2(mathcal{O}_L^S,mathbb{Z}(n))$ from the lead term of the Taylor series for the$S$-modified Artin $L$-function $L_{L/F}^S(s,psi)$ at $s=1-n$.

【 授权许可】

Unknown