English

Permanence criteria for semi-free profinite groups

Group Theory 2010-04-02 v2 Algebraic Geometry

Abstract

We introduce the condition of a profinite group being semi-free, which is more general than being free and more restrictive than being quasi-free. In particular, every projective semi-free profinite group is free. We prove that the usual permanence properties of free groups carry over to semi-free groups. Using this, we conclude that if k is a separably closed field, then many field extensions of k((x,y)) have free absolute Galois groups.

Keywords

Cite

@article{arxiv.0810.0845,
  title  = {Permanence criteria for semi-free profinite groups},
  author = {Lior Bary-Soroker and Dan Haran and David Harbater},
  journal= {arXiv preprint arXiv:0810.0845},
  year   = {2010}
}

Comments

24 pages

R2 v1 2026-06-21T11:27:30.211Z