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The Tame-Wild Principle For Discriminant Relations For Number Fields, John W. Jones, David P. Roberts
The Tame-Wild Principle For Discriminant Relations For Number Fields, John W. Jones, David P. Roberts
Mathematics Publications
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.