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 Zap. Nauchn. Sem. POMI, 1999, Volume 265, Pages 77–109 (Mi znsl1191)

Extensions with almost maximal depth of ramification

S. V. Vostokov, I. B. Zhukov, G. K. Pak

Saint-Petersburg State University

Abstract: The paper is devoted to classification of finite abelian extensions $L/K$ which satisfy the condition $[L:K]\mid\mathscr D_{L/K}.$ Here $K$ is a complete discretely valued field of characteristic 0 with an arbitrary residue field of prime characteristic $p$, $\mathscr D_{L/K}$ is the different of $L/K$. This condition means that the depth of ramification in $L/K$ has its “almost maximal” value. The condition appeared to play an important role in the study of additive Galois modules associated with the extension $L/K$.
The study is based on the use of the notion of independently ramified extensions, introduced by the authors. Two principal theorems are proven, describing almost maximally ramified extensions in the cases when the absolute ramification index $e$ is (resp. is not) divisible by $p-1$.

Full text: PDF file (311 kB)

English version:
Journal of Mathematical Sciences (New York), 2002, 112:3, 4285–4302

Bibliographic databases:

UDC: 512

Citation: S. V. Vostokov, I. B. Zhukov, G. K. Pak, “Extensions with almost maximal depth of ramification”, Problems in the theory of representations of algebras and groups. Part 6, Zap. Nauchn. Sem. POMI, 265, POMI, St. Petersburg, 1999, 77–109; J. Math. Sci. (New York), 112:3 (2002), 4285–4302

Citation in format AMSBIB
\Bibitem{VosZhuPak99} \by S.~V.~Vostokov, I.~B.~Zhukov, G.~K.~Pak \paper Extensions with almost maximal depth of ramification \inbook Problems in the theory of representations of algebras and groups. Part~6 \serial Zap. Nauchn. Sem. POMI \yr 1999 \vol 265 \pages 77--109 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl1191} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1757817} \zmath{https://zbmath.org/?q=an:1039.11084} \transl \jour J. Math. Sci. (New York) \yr 2002 \vol 112 \issue 3 \pages 4285--4302 \crossref{https://doi.org/10.1023/A:1020382616985} 

• http://mi.mathnet.ru/eng/znsl1191
• http://mi.mathnet.ru/eng/znsl/v265/p77

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This publication is cited in the following articles:
1. I. B. Zhukov, “Ramification in elementary abelian extensions”, J. Math. Sci. (N. Y.), 202:3 (2014), 404–409
2. St. Petersburg Math. J., 26:5 (2015), 695–740
3. Xiao L. Zhukov I., “Ramification of Higher Local Fields, Approaches and Questions”, Valuation Theory in Interaction, EMS Ser. Congr. Rep., ed. Campillo A. Kuhlmann F. Teissier B., Eur. Math. Soc., 2014, 600–656