Higher criteria for the regularity of a one-dimensional local field

Authors

  • 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; St Petersburg Electrotechnical University “LETI”, 5, ul. Professora Popova, StPetersburg, 197022, Russian Federation
  • Vladimir M. Polyakov St Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences, 27, nab. r. Fontanki, StPetersburg, 191023, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.205

Abstract

The concept of irregularity of formal modules in one-dimensional local fields is considered. A connection is obtained between the irregularity of all unramified extensions M/L and the ramification index e_(L/K) for a sufficiently wide class of formal groups. The notion of s-irregularity for natural s is introduced (generalization of the notion of irregularity to the case of roots [π^s]), and similar criteria for irregularity are proved for it for the case of generalized and relative formal Lubin—Tate modules.

Keywords:

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

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References

Литература

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Published

2022-07-06

How to Cite

Vostokov, S. V., Pital’, P. N., & Polyakov, V. M. (2022). Higher criteria for the regularity of a one-dimensional local field. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(2), 229–244. https://doi.org/10.21638/spbu01.2022.205

Issue

Vol. 9 No. 2 (2022)

Section

Mathematics

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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.