The tame-wild principle for discriminant relations for number fields

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.