Higher cyclotomic units for motivic cohomology. (English) Zbl 07443911

Summary: In the present article, we describe specific elements in a motivic cohomology group \(H^1_{\mathcal{M}} \bigl(\mathrm{Spec}\mathbb{Q} (\zeta_l), \mathbb{Z}(2) \bigr)\) of cyclotomic fields, which generate a subgroup of finite index for an odd prime \(l\). As \(H^1_{\mathcal{M}} \bigl(\mathrm{Spec}\mathbb{Q} (\zeta_l), \mathbb{Z}(1)\) is identified with the group of units in the ring of integers in \(\mathbb{Q} (\zeta_l)\) and cyclotomic units generate a subgroup of finite index, these elements play similar roles in the motivic cohomology group.


19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
11R70 \(K\)-theory of global fields
19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
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