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On function fields with free absolute Galois groups
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David Harbater
Published/Copyright:
June 16, 2009
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. Related results about quasi-free groups are also shown, in particular that the commutator subgroup of a quasi-free group is quasi-free.
Received: 2007-03-13
Revised: 2008-03-06
Published Online: 2009-06-16
Published in Print: 2009-July
© Walter de Gruyter Berlin · New York 2009
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Articles in the same Issue
- Ends of locally symmetric spaces with maximal bottom spectrum
- Subsystems of finite type and semigroup invariants of subshifts
- Explicit n-descent on elliptic curves, II. Geometry
- On function fields with free absolute Galois groups
- Ternary cyclotomic polynomials having a large coefficient
- The Minus Conjecture revisited
- On the moduli space of certain smooth codimension-one foliations of the 5-sphere by complex surfaces
- Arithmetic duality theorems for 1-motives over function fields
- Arithmetic duality theorems for 1-motives
