## 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.

### 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
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### References:

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