A Database of Number Fields

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Description

We describe an online database of number fields which accompanies this paper. The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.

Date Created
2013-11-30
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The Tame-Wild Principle for Discriminant Relations for Number Fields

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Description

Consider tuples (K1,…,Kr) of separable algebras over a common local or global number field F 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

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

Date Created
2013-11-30
Agent