On the analyticity of the maximal extension of a number field with prescribed ramification and splitting

On the analyticity of the maximal extension of a number field with prescribed ramification and splitting

We determine all the \(p\)-adic analytic groups that are realizable as Galois groups of the maximal pro-\(p\) extensions of number fields with prescribed ramification and splitting under an assumption which allows us to move away from the Tame Fontaine-Mazur conjecture.

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Veröffentlicht in:arXiv.org 2023-08
Hauptverfasser: Lim, Donghyeok, Maire, Christian
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Sprache:eng
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Number theory
Splitting
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description We determine all the \(p\)-adic analytic groups that are realizable as Galois groups of the maximal pro-\(p\) extensions of number fields with prescribed ramification and splitting under an assumption which allows us to move away from the Tame Fontaine-Mazur conjecture.
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subjects Number theory
Splitting
title On the analyticity of the maximal extension of a number field with prescribed ramification and splitting
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