Local Galois theory in dimension two: Second edition

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.

35 pages. Second edition to a 2005 Advanced in Math. paper, strengthening results from quasi-free groups to semi-free groups