Vol. 8, No. 3, 2014

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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

Consider tuples (K1,,Kr) of separable algebras over a common local or global number field F, with the Ki 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 KiF. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.

number field, discriminant, ramification
Mathematical Subject Classification 2010
Primary: 11S15
Secondary: 11S20, 11R32
Received: 13 December 2012
Revised: 11 September 2013
Accepted: 21 October 2013
Published: 31 May 2014
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