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
Abstract

Consider tuples $\left({K}_{1},\dots ,{K}_{r}\right)$ 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