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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     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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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/

[1] L. Xiao, I. Zhukov, Ramification in the imperfect residue field case, approaches and questions, http://math.usask.ca/fvk/Xiao-Zhukov.pdf

[2] S. Wewers, Fiercely ramified cyclic extensions of $p$-adic fields with imperfect residue field, arXiv: 1104.3785

[3] I. Fesenko, S. Vostokov, Local Fields And Their Extentions, Second edition, AMS, 2001

[4] M. Morrow, An introduction to higher dimensional local fields and adèles, http://math.uchicago.edu/~mmorrow/Morrow Intro to HLF.pdf

[5] A. Obus, R. Pries, “Wild cyclic-by-tame extensions”, J. Pure Appl. Algebra, 214 (2010), 565–573 | DOI | MR | Zbl

[6] H. L. Schmid, “Zur Arithmetik der zyklischen $p$-Korper”, J. für die reine und angew. Math., 176 (1937), 161–167

[7] L. Thomas, “Ramification groups in Artin–Schreier–Witt extensions”, J. de theorie des nombres de Bordeaux, 17:2 (2005), 689–720 | DOI | MR | Zbl

[8] J.-P. Serre, Local fields, Grad. Texts in Math., 67, Springer-Verlag, New York, 1979 | DOI | MR | Zbl