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Permanence criteria for semi-free profinite groups |
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| Authors: | Lior Bary-Soroker Dan Haran David Harbater |
| Institution: | 1. Institute of Mathematics, Hebrew University, Giv’at-Ram, 91904, Jerusalem, Israel 2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel 3. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA |
| 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. |
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