Preview

Chebyshevskii Sbornik

Advanced search

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 Vostokov
Saint Petersburg State University
Russian Federation
Doctor of Physical and Mathematical Sciences, Professor


Igor Borisovich Zhukov
Saint Petersburg State University
Russian Federation
Doctor of Physical and Mathematical Sciences


Olga Yur’evna Ivanova
Saint Petersburg State University
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

Views: 253


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2226-8383 (Print)