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 Zap. Nauchn. Sem. POMI, 2017, Volume 455, Pages 52–66 (Mi znsl6406)

Construction of cyclic extensions of degree $p^2$ for a complete field

I. Zhukova, E. Lysenkob

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Electrotechnical University "LETI", St. Petersburg, Russia

Abstract: In the present paper we embed a given cyclic extension of degree $p$ of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic $p>0$ into a cyclic extension of degree $p^2$. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension.

Key words and phrases: complete discrete valuation field, cyclic extension, ramification, ramification jump.

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Document Type: Article
UDC: 512.62

Citation: I. Zhukov, E. Lysenko, “Construction of cyclic extensions of degree $p^2$ for a complete field”, Problems in the theory of representations of algebras and groups. Part 31, Zap. Nauchn. Sem. POMI, 455, POMI, St. Petersburg, 2017, 52–66

Citation in format AMSBIB
\Bibitem{ZhuLys17} \by I.~Zhukov, E.~Lysenko \paper Construction of cyclic extensions of degree $p^2$ for a~complete field \inbook Problems in the theory of representations of algebras and groups. Part~31 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 455 \pages 52--66 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6406}