Lecture Notes in Mathematics Volume 1240, 1987, pp 165-195
Date: 11 Sep 2006

Galois coverings of the arithmetic line

* Final gross prices may vary according to local VAT.

Get Access

Abstract

This paper concerns Galois branched coverings of the line, first over the complex numbers and then over the p-adics. We construct such covers with arbitrary Galois group, and then descend these to covers defined over number fields. In particular, every finite group is shown to occur as a Galois group over \(\underline {\hat O} _p (t)\) . This is a consequence of a more general result that also implies that complete local domains other than fields are never Hilbertian — thus answering a question of Lang.

Supported in part by a Sloan Fellowship and NSF grant #MCS83-02068.