Local Galois theory in dimension two: Second edition

Details Local Galois theory in dimension two: Second edition Local Galois theory in dimension two: Second edition

2009-07-17

arxiv.org/abs/0907.3082v1

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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