Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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HIGHER CYCLOTOMIC UNITS FOR MOTIVIC COHOMOLOGY

  • Myung, Sung (Department of Mathematics Education Inha University)
  • Received : 2013.04.13
  • Accepted : 2013.09.13
  • Published : 2013.09.30
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Abstract

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

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References

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