Local Galois theory in dimension two: Second edition
Algebraic Geometry
2009-07-20 v1 Group Theory
Abstract
We prove a generalization of Shafarevich's Conjecture for fields of Laurent series in two variables over an arbitrary field. While not projective, the absolute Galois group of such a field is shown to be semi-free. We also show that the function field of a smooth projective curve over a large field has semi-free absolute Galois group. In the first edition of this paper it was shown that these groups are quasi-free, which is weaker.
Keywords
Cite
@article{arxiv.0907.3082,
title = {Local Galois theory in dimension two: Second edition},
author = {David Harbater and Katherine F. Stevenson},
journal= {arXiv preprint arXiv:0907.3082},
year = {2009}
}
Comments
35 pages. Second edition to a 2005 Advanced in Math. paper, strengthening results from quasi-free groups to semi-free groups