%0 Journal Article
%T Projective pairs of profinite groups
%A Lior Bary-Soroker
%J Mathematics
%D 2008
%I arXiv
%X We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish the connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic extension of a PAC field K. Then M/K is PAC if and only if the corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective. Moreover any projective pair can be realized as absolute Galois groups of a PAC extension of a PAC field. Using this characterization we construct new examples of PAC extensions of relatively small fields, e.g., unbounded abelian extensions of the rational numbers.
%U http://arxiv.org/abs/0810.5440v1