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Abelian p-extensions of an absolutely unramified field

✍ Scribed by I. B. Zhukov

Publisher
Springer US
Year
1993
Tongue
English
Weight
407 KB
Volume
63
Category
Article
ISSN
1573-8795

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Assume that \(K\) is either a totally real or a totally imaginary number field. Let \(F\) be the maximal unramified elementary abelian 2-extension of \(K\) and \([F: K]=2^{n}\). The purpose of this paper is to describe a family of cubic cyclic extension of \(K\). We have constructed an unramified ab

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We study the deformation theory of Galois representations whose restriction to every decomposition subgroup is abelian. As an application, we construct unramified non-solvable extensions over the field obtained by adjoining all p-power roots of unity to the field of rational numbers.