On the asymptotics of elementary-abelian extensions of local and global function fields
Number Theory
2025-06-06 v3
Abstract
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic . 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.
Cite
@article{arxiv.2408.16394,
title = {On the asymptotics of elementary-abelian extensions of local and global function fields},
author = {Nicolas Potthast},
journal= {arXiv preprint arXiv:2408.16394},
year = {2025}
}
Comments
51 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