Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.
@article{bwmeta1.element.doi-10_2478_v10062-012-0027-8,
author = {Akram Lbekkouri},
title = {Some results on local fields},
journal = {Annales UMCS, Mathematica},
volume = {67},
year = {2013},
pages = {17-32},
zbl = {1296.11158},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0027-8}
}
Akram Lbekkouri. Some results on local fields. Annales UMCS, Mathematica, Tome 67 (2013) pp. 17-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0027-8/
[1] Abbes, A., Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (5) (2002), 879-920.[Crossref][WoS] | Zbl 1084.11064
[2] Artin, E., Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1942. | Zbl 0060.04813
[3] Hazewinkel, M., Local class field theory is easy, Adv. Math. 18 (1975), 148-181. | Zbl 0312.12022
[4] Lbekkouri, A., On the construction of normal wildly ramified over Qp, (p = 2), Arch. Math. (Basel) 93 (2009), 331-344.[Crossref][WoS] | Zbl 1233.11123
[5] Ribes, L., Zalesskii, P., Profinite Groups, Springer-Verlag, Berlin, 2000. | Zbl 0949.20017
[6] Rotman, J. J., An Introduction to the Theory of Group, Springer-Verlag, New York, 1995. | Zbl 0810.20001
[7] Serre, J.-P., Local Fields, Springer-Verlag, New York-Berlin, 1979.
[8] Zariski, O., Samuel, P., Commutative Algebra. Volume II, Springer-Verlag, New York- Heidelberg, 1975. | Zbl 0313.13001
[9] Zhukov, I. B., On ramification theory in the imperfect residue field case, Preprint No. 98-02, Nottingham Univ., 1998. Proceedings of the conference: Ramification Theory of Arithmetic Schemes (Luminy, 1999) (ed. B. Erez), http://family239.narod.ru/math/publ.htm.