Hurwitz monodromy and full number fields

Roberts, David; Venkatesh, Akshay

doi:10.2140/ant.2015.9.511

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Hurwitz monodromy and full number fields

David P. Roberts and Akshay Venkatesh

Vol. 9 (2015), No. 3, 511–545

DOI: 10.2140/ant.2015.9.511

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 $A_{m}$ or $S_{m}$ number fields unramified away from ${2, 3, 5}$ .

Keywords

number fields, Hurwitz spaces

Mathematical Subject Classification 2010

Primary: 14D05

Secondary: 20F36, 11R21

Milestones

Received: 28 January 2014

Revised: 8 January 2015

Accepted: 18 February 2015

Published: 17 April 2015

Authors

David P. Roberts
Division of Science and Mathematics University of Minnesota Morris, MN 56267 United States

Akshay Venkatesh
Department of Mathematics Building 380 Stanford University Stanford, CA 94305 United States

Vol. 9, No. 3, 2015