2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115532We 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.18 pagesAlgebraic GeometryNumber Theory12E30; 14H30text