Regular formal modules in local fields and irregularly degree

Authors

  • Natalya K. Vlaskina St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Sergei V. Vostokov St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Petr N. Pital’ St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Aleksey E. Tsybyshiev St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27, nab. r. Fontanki, St. Petersburg, 191029, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2020.402

Abstract

In this paper we investigate the irregular degree of finite not ramified local field extantions with respect to a polynomial formal group and in the multiplicative case. There was found necessary and sufficient conditions for the existence of primitive roots of ps power from 1 and (endomorphism [ps]Fm) in L-th unramified extension of the local field K (for all positive integer s). These conditions depend only on the ramification index of the maximal abelian subextension of the field K Ka/Qp.

Keywords:

regular formal modules, formal modules, formal groups, local fields

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References

Литература

1. Боревич З. И. О регулярных локальных полях // Вестн. Ленингр. ун-та. 1962. Вып. 1. С. 142–145.

2. Касселс Дж., Фрёлих А. Алгебраическая теория чисел. 1969.

3. Востоков С. В., Некрасов И. И. Формальныймодуль Любина — Тейта в циклическом неразветвленном p-расширении как модуль Галуа // Зап. научн. сем. ПОМИ. 2014. Т. 430. P. 61–66.

4. Власьев С. М., Востоков С. В., Горшков А. А. Регулярные формальные модули в одномерных локальных полях // Вестн. С.-Петерб. ун-та. Сер. 1. Математика. Механика. Астрономия. 2016. Т. 3 (61). Вып. 4. С. 544–551. https://doi.org/10.21638/11701/spbu01.2016.403

References

1. Borevich Z. I., “About regular local fields”, Vestn. of Leningrad Univ., 142–145 (1962). (In Russian)

2. Cassels J. W. S., Frohlich A., Algebraic Number Theory (Academic Press, 1969).

3. Vostokov V., Nekrasov I. I., “Lubin — Tate formal module in a cyclic unramified p-extension as Galois module”, J. Math. Sci. (N. Y.) 219(3), 375–379 (2016). ttps://doi.org/10.1007/s10958-016-3113-6

4. Vlassiev S. M., Vostokov S. V., Gorshkov A. A., “Regular formal modules in onedimensional local fields”, Vestnik St. Petersb. Univ. Math. 49, 313–319 (2016). https://doi.org/10.3103/S1063454116040142

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Published

2020-12-27

How to Cite

Vlaskina, N. K., Vostokov, S. V., Pital’, P. N., & Tsybyshiev, A. E. (2020). Regular formal modules in local fields and irregularly degree. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(4), 588–596. https://doi.org/10.21638/spbu01.2020.402

Issue

Vol. 7 No. 4 (2020)

Section

On the anniversary of S. V. Vostokov

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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