Algebra & Number Theory
Consider tuples ( K1 , … , Kr ) of separable algebras over a common local or global number field F1, 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 Ki ∕ F . We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.
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John W. Jones and David P. Roberts. The tame-wild principle for discriminant relations for number fields. Algebra and Number Theory 8 (2014), no. 3, 609-645.