On explicit constructions of extensions of complete fields
https://doi.org/10.22405/2226-8383-2025-26-4-108-122
Abstract
This article is devoted to the use of sequences of Artin-Schreier equations to defining 𝑝-Galois extensions of complete discrete valuation fields of mixed characteristic. Along with a review of
known results in this area, some new results for abelian 2-extensions are obtained. Furthermore, the study of almost maximally ramified extensions introduced by S. V. Vostokov in his study of additive Galois modules is continued. It is proved that if the Galois group of such an extension has period p, it is necessarily abelian.
About the Authors
Igor Borisovich Zhukov
Saint Petersburg State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Olga Yur’evna Ivanova
Saint Petersburg State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Zhukov I.B., Ivanova O.Yu. On explicit constructions of extensions of complete fields. Chebyshevskii Sbornik. 2025;26(4):108-122. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-108-122
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