The absolute Galois groups of finite extensions of ℝ(t)

Dan Haran; M. Jarden

doi:10.1007/s00013-007-2386-x

The absolute Galois groups of finite extensions of ℝ(t)

Dan Haran^*
, M. Jarden

^*Corresponding author for this work

School of Mathematical Sciences

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

1 Scopus citations

Abstract

Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ≈ Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card (R) if L is not formally real.

Original language	English
Pages (from-to)	524-529
Number of pages	6
Journal	Archiv der Mathematik
Volume	89
Issue number	6
DOIs	https://doi.org/10.1007/s00013-007-2386-x
State	Published - Dec 2007

Funding

Funders
Minerva Foundation
Tel Aviv University

Keywords

Absolute Galois group
Free profinite group
Kurosh subgroup theorem
Real closed field

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10.1007/s00013-007-2386-x

Cite this

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title = "The absolute Galois groups of finite extensions of ℝ(t)",

abstract = "Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ≈ Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card (R) if L is not formally real.",

keywords = "Absolute Galois group, Free profinite group, Kurosh subgroup theorem, Real closed field",

author = "Dan Haran and M. Jarden",

note = "Funding Information: Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation.",

year = "2007",

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AU - Haran, Dan

AU - Jarden, M.

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N2 - Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ≈ Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card (R) if L is not formally real.

AB - Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ≈ Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card (R) if L is not formally real.

KW - Absolute Galois group

KW - Free profinite group

KW - Kurosh subgroup theorem

KW - Real closed field

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JO - Archiv der Mathematik

JF - Archiv der Mathematik

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ER -

The absolute Galois groups of finite extensions of ℝ(t)

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Keywords

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