Geodesic
Continuability of cyclic extensions of complete discrete valuation fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 5-17 
V. G. Boitsov; I. B. Zhukov. Continuability of cyclic extensions of complete discrete valuation fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a0/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For a complete discrete valuation field $K$ of characteristic 0 with the residue field of characteristic $p>0$ consider the embedding problem of a given cyclic extension $M/K$ of degree $p$ into a cyclic extension of degree $p^n$ for various $n$. Let $c(M/K)$ be the maximal $n$ such that this embedding problem has a solution. In this paper we consider relations between $c(M/K)$ and $c(LM/L)$ where $L/K$ is a given extension linearly disjoint with $M/K$.

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