Inaba extension of complete field of characteristic 0
https://doi.org/10.22405/2226-8383-2020-21-3-59-67
About the Authors
Sergey Vladimirovich VostokovRussian Federation
Doctor of Physical and Mathematical Sciences, Professor
Igor Borisovich Zhukov
Russian Federation
Doctor of Physical and Mathematical Sciences
Olga Yur’evna Ivanova
Russian Federation
Candidate of Physical and Mathematical Sciences
References
1. Cassels, J. W. S., Frohlich, A., 1967, ‘’Algebraic Number Theory’’, Academic Press, London and New-York.
2. Fesenko, I.\,B., Vostokov, S. V., Zhukov I. B., 1990, ``On the theory of multidimensional local fields. Methods and constructions'', Algebra i Analiz vol. 2, № 4. pp. 91-118.
3. Fesenko I. B., Vostokov, S. V., 2002,``Local fields and their extensions. A constructive approach'',Second edition, AMS, Providence, RI.4. Hyodo, O., 1987,Wild ramification in the imperfect residue field case ''Adv. Stud. Pure Math, vol. 12, pp. 287-314.
4. Inaba, E., 1961,``On matrix equations for Galois extensions of fields with characteristic $p$'', Natur. Sci. Rep. Ochanomizu Univ., vol. 12, pp. 26-36.
5. Inaba, E., 1962,``On generalized Artin-Schreier equations'',{\em Natur. Sci. Rep. Ochanomizu Univ.}, vol. 13, № 2, pp. 1-13.
6. Zhukov, I. B., Lysenko, E.F., 2018,``Construction of cyclic extensions of degree $p^2$ for a complete field'', vol. 234(2), pp. 148–157.
7. MacKenzie, R. E., Whaples, G., 1956,``Artin–Schreier equations in characteristic zero'',Amer. J. Math, vol. 78, pp. 473-485.
8. Madunts, A. I., 2004,``Lubin–Tate Formal Groups over the Ring of Integers of a Multidimensional Local Field'', J. Math. Sci., vol. 120(4) pp. 1609–1612.
9. Miki, H., 1974,``On $Z_p$-extensions of complete p-adic power series fields and function fields'', J. Fac. Sci. Univ. Tokyo, Sect 1A, vol. 21, pp. 377-393.
10. Vostokov, S. V., Zhukov, I. B., Pak, G.K., 1999,``Extensions with almost maximal depth of ramification'', J. Math. Sci., vol. 112(3), pp. 4285-4302.
11. Vostokov, S. V., Zhukov, I. B., 1995,``Some approaches to the construction of abelian extensions for $\mathfrak p$-adic fields'', Proceedings of the St. Petersburg Mathematical Society, Vol. III, 157–174,Amer. Math. Soc. Transl. Ser. 2, 166, Amer. Math. Soc., Providence, RI, 1995.
12. Xiao, L., Zhukov, I., 2014,``Ramification in the imperfect residue field case, approaches and questions'', Algebra i Analiz, vol. 26, № 5. pp. 695-740.
13. Zhukov, I. B., 1995,``Structure theorems for complete fields'', Proceedings of the St. Petersburg Mathematical Society, Vol. III, 175–192, Amer. Math. Soc. Transl. Ser. 2, 166, Amer. Math. Soc., Providence, RI, 1995.
14. Zhukov, I., 2000,``Explicit abelian extensions of complete discrete valuation fields'', in book: Fesenko, I., Kurihara, M. (eds.) Invitation to Higher Local Fields. Geometry and Topology Monographs, vol. 3, pp. 117-122.
Review
For citations:
Vostokov S.V., Zhukov I.B., Ivanova O.Yu. Inaba extension of complete field of characteristic 0. Chebyshevskii Sbornik. 2020;21(3):59-67. https://doi.org/10.22405/2226-8383-2020-21-3-59-67