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

Myung, Sung

Korean J. Math. 21, No. 3, 331-344 (2013).

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.

MSC:

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)

Keywords:

cyclomotic units; motivic cohomology

References:

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[11]	Department of Mathematics Education Inha University Incheon 402-751, Korea E-mail : [e-mail]