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Galois coverings of the arithmetic line

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Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1240))

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 . 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.

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Authors and Affiliations

  1. University of Pennsylvania, USA

    David Harbater

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  1. David Harbater
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David V. Chudnovsky Gregory V. Chudnovsky Harvey Cohn Melvyn B. Nathanson

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© 1987 Springer-Verlag

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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. https://doi.org/10.1007/BFb0072980

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  • DOI: https://doi.org/10.1007/BFb0072980

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17669-5

  • Online ISBN: 978-3-540-47756-3

  • eBook Packages: Springer Book Archive

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