HIGHER CYCLOTOMIC UNITS FOR MOTIVIC COHOMOLOGY

Abstract

In the present article, we describe specific elements in a motivic cohomology group $H^1_{M} \bigl( Spec Q (\zeta_l), \, Z(2) \bigr)$ of cyclotomic fields, which generate a subgroup of finite index for an odd prime $l$. As $H^1_{M} \bigl( Spec Q (\zeta_l), \, Z(1) \bigr)$ 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.