Geodesic
Ramification of cyclic extensions of degree $p^2$ of complete discrete valuation fields of prime characteristic $p$ with imperfect residue field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 153-172 
E. F. Lysenko. Ramification of cyclic extensions of degree $p^2$ of complete discrete valuation fields of prime characteristic $p$ with imperfect residue field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 153-172. http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a7/
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     title = {Ramification of cyclic extensions of degree $p^2$ of complete discrete valuation fields of prime characteristic~$p$ with imperfect residue field},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the present paper we study ramification invariants of complete discrete valuation fields of prime characteristic $p$ with imperfect residue field. Using Witt vectors we calculate ramification breaks of cyclic extensions of degree $p^2$ of such field. We obtain necessary and sufficient conditions for a pair of natural numbers to be ramification breaks of a cyclic extension of degree $p^2$.

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