Number Theory pp 165-195

Galois coverings of the arithmetic line

  • David Harbater
Conference paper

DOI: 10.1007/BFb0072980

Part of the Lecture Notes in Mathematics book series (LNM, volume 1240)
Cite this paper as:
Harbater D. (1987) Galois coverings of the arithmetic line. In: Chudnovsky D.V., Chudnovsky G.V., Cohn H., Nathanson M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1240. Springer, Berlin, Heidelberg

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 Open image in new window. 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.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • David Harbater
    • 1
  1. 1.University of PennsylvaniaUSA

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