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On function fields with free absolute Galois groups

David Harbater
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Abstract

We prove that certain fields have the property that their absolute Galois groups are free as profinite groups: the function field of a real curve with no real points; the maximal abelian extension of a 2-variable Laurent series field over a separably closed field; and the maximal abelian extension of the function field of a curve over a finite field. These results are related to generalizations of Shafarevich's conjecture.

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David Harbater. 2006-08-23. On function fields with free absolute Galois groups. https://arxiv.org/abs/math/0608584

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