Hurwitz monodromy and full number fields

David P. Roberts, Akshay Venkatesh

    Research output: Contribution to journalArticlepeer-review

    3 Scopus citations

    Abstract

    We give conditions for the monodromy group of a Hurwitz space over the configuration space of branch points to be the full alternating or symmetric group on the degree. Specializing the resulting coverings suggests the existence of many number fields with surprisingly little ramification-for example, the existence of infinitely many Am or Sm number fields unramified away from {2; 3; 5}.

    Original languageEnglish (US)
    Pages (from-to)511-545
    Number of pages35
    JournalAlgebra and Number Theory
    Volume9
    Issue number3
    DOIs
    StatePublished - Jul 11 2015

    Keywords

    • Hurwitz spaces
    • Number fields

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