Geodesic
Explicit constructions of extensions of complete fields of characteristic $0$
Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 179-196

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This survey article is devoted to $p$-extensions of complete discrete valuation fields of mixed characteristic where $p$ is the characteristic of the residue field. It is known that any totally ramified Galois extension with a non-maximal ramification jump can be determined by an Artin-Schreier equation, and the upper bound for the ramification jump corresponds to the lower bound of the valuation in the right-hand side of the equation. The problem of construction of extensions with arbitrary Galois groups is not solved.
Keywords: discrete valuation field, ramification jump, Artin-Schreier equation. 
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     title = {Explicit constructions of extensions of complete fields of characteristic $0$},
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I. B. Zhukov; O. Yu. Ivanova. Explicit constructions of extensions of complete fields of characteristic $0$. Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 179-196. http://geodesic.mathdoc.fr/item/CHEB_2023_24_2_a8/