The tame-wild principle for discriminant relations for number fields

Jones, John; Roberts, David

doi:10.2140/ant.2014.8.609

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The tame-wild principle for discriminant relations for number fields

John W. Jones and David P. Roberts

Vol. 8 (2014), No. 3, 609–645

DOI: 10.2140/ant.2014.8.609

Abstract

Consider tuples $(K_{1}, \dots, K_{r})$ of separable algebras over a common local or global number field $F$ , with the $K_{i}$ related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of $K_{i} ∕ F$ . We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.

Keywords

number field, discriminant, ramification

Mathematical Subject Classification 2010

Primary: 11S15

Secondary: 11S20, 11R32

Milestones

Received: 13 December 2012

Revised: 11 September 2013

Accepted: 21 October 2013

Published: 31 May 2014

Authors

John W. Jones
School of Mathematical and Statistical Sciences Arizona State University P.O. Box 871804 Tempe, AZ 85287-1804 United States

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

Vol. 8, No. 3, 2014