局部与全局函数域的半直积扩张的渐近分析
数论
2025-06-06 v3
摘要
我们确定特征为 的局部与全局函数域的野坍缩初等-阿贝尔扩张的判别式分布。对于局部与有理函数域，我们给出判别式固定判别子数的初等-阿贝尔扩张的精确公式，这描述了一种局部-全局原理。
引用
@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}
}
备注
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