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Capitulation in the cyclotomic ℤ2 extension of CM number fields

Published online by Cambridge University Press:  12 February 2018

KATHARINA MÜLLER
KATHARINA MÜLLER*
Affiliation:
Mathematisches Institut, Georg–August–Universität Göttingen, e-mail: [email protected]
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Abstract

Let 𝕂n be the intermediate steps in the cyclotomic ℤp-extension of a CM number field 𝕂. For p ⧧ 2 the minus part of the p-class groups is given by An− = $\frac{1}{2}$(1 − j)An. We will give a new definition of the minus part for p = 2 and will prove that there is no finite submodule in lim∞←nAn−. Furthermore we will show that μ = 0 if and only if μ− = 0 in this new definition.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 2 , March 2019 , pp. 371 - 380
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

REFERENCE

[1] Washington, L. C. Introduction to Cyclotomic Fields. Graduate Texts in Math. 83 (Springer, 1982).Google Scholar