Abstract

The variation in the irregularity degree of a finite unramified local field extensions of a local field is investigated with respect to a polynomial formal group and in the multiplicative case. The necessary and sufficient conditions for the existence of the p^sth primitive roots of the p^sth power of 1 and (endomorphism \({{[{{p}^{s}}]}_{{{{F}_{m}}}}}\)) in the Lth unramified extension of the local field K (for all positive integers s) are found. The conditions depend only on the ramification index of the maximal Abelian subextension of the field K K_a/\({{\mathbb{Q}}_{p}}\).

中文翻译：

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局部领域的不规则度和正规形式模块

摘要

针对多项式形式组和可乘情况，研究了局部场的有限未分支局部场扩展的不规则度的变化。对于存在的必要和充分条件p^小号的的第原始根p ^š的1次方和（自同态\（{{[{{P} ^ {S}}]} _ {{{{F} _ {m}}}}}}）））在局部字段K的第L个无分支扩展中找到（对于所有正整数s）。条件仅取决于字段K K _a / \（{{\ mathbb {Q}} _ {p}} \）的最大Abelian次扩展的分枝索引。