Finitely generated pro-p Galois groups of p-Henselian fields

Ido Efrat

doi:10.1016/S0022-4049(98)00033-4

Finitely generated pro-p Galois groups of p-Henselian fields

Ido Efrat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Let p be a prime number, let K be a field of characteristic 0 containing a primitive root of unity of order p. Also let υ be a p-henselian (Krull) valuation on K with residue characteristic p. We determine the structure of the maximal pro-p Galois group G_K(p) of K, provided that it is finitely generated. This extends classical results of Demuškin, Serre and Labute.

Original language	English
Pages (from-to)	215-228
Number of pages	14
Journal	Journal of Pure and Applied Algebra
Volume	138
Issue number	3
DOIs	https://doi.org/10.1016/S0022-4049(98)00033-4
State	Published - 27 May 1999

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(98)00033-4

Cite this

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abstract = "Let p be a prime number, let K be a field of characteristic 0 containing a primitive root of unity of order p. Also let υ be a p-henselian (Krull) valuation on K with residue characteristic p. We determine the structure of the maximal pro-p Galois group GK(p) of K, provided that it is finitely generated. This extends classical results of Demu{\v s}kin, Serre and Labute.",

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N2 - Let p be a prime number, let K be a field of characteristic 0 containing a primitive root of unity of order p. Also let υ be a p-henselian (Krull) valuation on K with residue characteristic p. We determine the structure of the maximal pro-p Galois group GK(p) of K, provided that it is finitely generated. This extends classical results of Demuškin, Serre and Labute.

AB - Let p be a prime number, let K be a field of characteristic 0 containing a primitive root of unity of order p. Also let υ be a p-henselian (Krull) valuation on K with residue characteristic p. We determine the structure of the maximal pro-p Galois group GK(p) of K, provided that it is finitely generated. This extends classical results of Demuškin, Serre and Labute.

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U2 - 10.1016/S0022-4049(98)00033-4

DO - 10.1016/S0022-4049(98)00033-4

M3 - Article

AN - SCOPUS:0033609233

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VL - 138

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EP - 228

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -

Finitely generated pro-p Galois groups of p-Henselian fields

Abstract

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