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Galois coverings of the arithmetic line

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Finite Group
  • Galois Group
  • Number Field
  • Galois Extension
  • Branch Locus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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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

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