Analysis of discriminants in elementary-abelian extensions, revealing local-global principles in function fields.
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic p p . For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.
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Nicolas Potthast (2025) studied this question.
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