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
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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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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/

[1] I. B. Fesenko, S. V. Vostokov, “Local fields and their extensions”, Translations of Mathematical Monographs, 121, AMS, Providence, RI, 2002 | MR | Zbl

[2] O. Hyodo, “Wild ramification in the imperfect residue field case”, Adv. Studies in Pure Math., 12 (1987), 287–314 | MR | Zbl

[3] H. Miki, “On $Z_p$-extensions of complete p-adic power series fields and function fields”, J. Fac. Sci. Univ. Tokyo, Sect. IA, 2 (1974), 377–393 | MR

[4] I. B. Zhukov, “Strukturnaya teorema dlya polnykh polei”, Trudy Sankt-Peterburgskogo mat. obschestva, 3, 1995, 215–234 | MR | Zbl

[5] I. B. Zhukov, M. V. Koroteev, “Ustranenie vysshego vetvleniya”, Algebra i analiz, 11:6 (1999), 153–177 | MR | Zbl