TY - JOUR

T1 - Degree of Irregularity and Regular Formal Modules in Local Fields

AU - Vlaskina, N. K.

AU - Vostokov, S. V.

AU - Pital’, P. N.

AU - Tsybyshev, A. E.

N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd.

PY - 2020/10

Y1 - 2020/10

N2 - 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]Fm) 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 KKa/Qp.

AB - 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]Fm) 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 KKa/Qp.

KW - formal groups

KW - formal modules

KW - local fields

KW - regular formal modules

UR - http://www.scopus.com/inward/record.url?scp=85097567830&partnerID=8YFLogxK

U2 - 10.1134/S106345412004010X

DO - 10.1134/S106345412004010X

M3 - Article

AN - SCOPUS:85097567830

VL - 53

SP - 398

EP - 403

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -