Abstract : This talk will present some results related to Shafarevich's conjecture on absolute Galois groups. In particular, the absolute Galois groups of the following fields 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.