Vestnik St. Petersburg University, Mathematics ( IF 0.4 ) Pub Date : 2020-12-13 , DOI: 10.1134/s106345412004010x N. K. Vlaskina , S. V. Vostokov , P. N. Pital’ , A. E. Tsybyshev
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 psth primitive roots of the psth 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 Ka/\({{\mathbb{Q}}_{p}}\).
中文翻译:
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。