Higher cyclotomic units for motivic cohomology

Abstract

In the present article, we describe specific elements in a motivic cohomology group $H_M^1(SpecQ({\zeta }_l),Z(2))$ of cyclotomic fields,
which generate a subgroup of finite index for an odd prime $l$. As $H_M^1(SpecQ({\zeta }_l),Z(1))$ is identified with the group of units in the ring of integers
in $Q({\zeta }_l)$ and cyclotomic units generate a subgroup of finite index, these elements play similar roles in the motivic cohomology group.