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arXiv · 0907.3082

Local Galois theory in dimension two: Second edition

David Harbater·Katherine F. Stevenson
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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.

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BibTeXRIS

David Harbater, Katherine F. Stevenson. 2009-07-17. Local Galois theory in dimension two: Second edition. https://arxiv.org/abs/0907.3082

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