Some results on local fields

Akram Lbekkouri

Abstract


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.

Keywords


Local fields; local number fields; Wild ramification; intermediate extension; standard p-over-extensions; semi-direct product; inertia group.

Full Text:

PDF

References


Abbes, A., Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (5) (2002), 879–920.

Artin, E., Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1942.

Hazewinkel, M., Local class field theory is easy, Adv. Math. 18 (1975), 148–181.

Lbekkouri, A., On the construction of normal wildly ramified over (mathbb{Q}_p), ((p neq 2)), Arch. Math. (Basel) 93 (2009), 331–344.

Ribes, L., Zalesskii, P., Profinite Groups, Springer-Verlag, Berlin, 2000.

Rotman, J. J., An Introduction to the Theory of Group, Springer-Verlag, New York, 1995.

Serre, J.-P., Local Fields, Springer-Verlag, New York–Berlin, 1979.

Zariski, O., Samuel, P., Commutative Algebra. Volume II, Springer-Verlag, New York–Heidelberg, 1975.

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.




DOI: http://dx.doi.org/10.2478/v10062-012-0027-8
Date of publication: 2015-07-15 00:00:00
Date of submission: 2016-01-12 09:10:44


Statistics


Total abstract view - 832
Downloads (from 2020-06-17) - PDF - 465

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Akram Lbekkouri