Local-global Galois theory of arithmetic function fields
Abstract
We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the local absolute Galois group to inject into the global absolute Galois group. As an application we obtain a local-global principle for the index of a variety over such a function field. In this context we also study algebraic versions of van Kampen's theorem, describing the global absolute Galois group as a pushout of local absolute Galois groups.
Cite
@article{arxiv.1710.03635,
title = {Local-global Galois theory of arithmetic function fields},
author = {David Harbater and Julia Hartmann and Daniel Krashen and R. Parimala and V. Suresh},
journal= {arXiv preprint arXiv:1710.03635},
year = {2018}
}
Comments
26 pages. Some reorganization of Section 3.2, with a new remark; notation in Section 3.3 for absolute Galois groupoids has been modified and made more consistent; slightly expanded introduction