On the asymptotics of elementary-abelian extensions of local and global function fields

Abstract

We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. 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.

arXiv comment51 pages; the main result of the article is now stated in the introductory chapter (Theorem 1.1) and the order of the introduction has been adapted, a self-contained statement of the applied inclusion-exclusion principle has been added (Lemma 5.5), Remark 3.9 from the previous version has been removed, other minor changes; to appear in Transactions of the American Mathematical Society

References in corpus (3)

• On the probabilities of local behaviors in abelian field extensions
• Distribution of Artin-Schreier extensions
• Distribution of Artin-Schreier-Witt extensions