A galois-theoretic characterization of p-adically closed fields

Ido Efrat

doi:10.1007/BF02761651

A galois-theoretic characterization of p-adically closed fields

Ido Efrat

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Abstract

Let p be an odd prime, K a field, and G_K its absolute Galois group. It is shown that K is p-adically closed if and only if G_K is isomorphic to an open subgroup of {Mathematical expression}. It is also shown that if {Mathematical expression}, with q=p^r, then K has a non-trivial henselian valuation.

Original language	English
Pages (from-to)	273-284
Number of pages	12
Journal	Israel Journal of Mathematics
Volume	91
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02761651
State	Published - 1 Oct 1995
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02761651

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title = "A galois-theoretic characterization of p-adically closed fields",

abstract = "Let p be an odd prime, K a field, and G K its absolute Galois group. It is shown that K is p-adically closed if and only if G K is isomorphic to an open subgroup of {Mathematical expression}. It is also shown that if {Mathematical expression}, with q=p r, then K has a non-trivial henselian valuation.",

author = "Ido Efrat",

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N2 - Let p be an odd prime, K a field, and G K its absolute Galois group. It is shown that K is p-adically closed if and only if G K is isomorphic to an open subgroup of {Mathematical expression}. It is also shown that if {Mathematical expression}, with q=p r, then K has a non-trivial henselian valuation.

AB - Let p be an odd prime, K a field, and G K its absolute Galois group. It is shown that K is p-adically closed if and only if G K is isomorphic to an open subgroup of {Mathematical expression}. It is also shown that if {Mathematical expression}, with q=p r, then K has a non-trivial henselian valuation.

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EP - 284

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1-3

ER -

A galois-theoretic characterization of p-adically closed fields

Abstract

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