Some results on local fields

Akram Lbekkouri

Annales UMCS, Mathematica (2013)

  • Volume: 67, Issue: 2, page 17-32
  • ISSN: 2083-7402

Abstract

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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.

How to cite

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Akram Lbekkouri. "Some results on local fields." Annales UMCS, Mathematica 67.2 (2013): 17-32. <http://eudml.org/doc/267875>.

@article{AkramLbekkouri2013,
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.},
author = {Akram Lbekkouri},
journal = {Annales UMCS, Mathematica},
keywords = {Local fields; local number fields; Wild ramification; intermediate extension; standard p-over-extensions; semi-direct product; inertia group; local fields; wild ramification; standard -over-extensions},
language = {eng},
number = {2},
pages = {17-32},
title = {Some results on local fields},
url = {http://eudml.org/doc/267875},
volume = {67},
year = {2013},
}

TY - JOUR
AU - Akram Lbekkouri
TI - Some results on local fields
JO - Annales UMCS, Mathematica
PY - 2013
VL - 67
IS - 2
SP - 17
EP - 32
AB - 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.
LA - eng
KW - Local fields; local number fields; Wild ramification; intermediate extension; standard p-over-extensions; semi-direct product; inertia group; local fields; wild ramification; standard -over-extensions
UR - http://eudml.org/doc/267875
ER -

References

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  1. [1] Abbes, A., Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (5) (2002), 879-920.[Crossref][WoS] Zbl1084.11064
  2. [2] Artin, E., Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1942. Zbl0060.04813
  3. [3] Hazewinkel, M., Local class field theory is easy, Adv. Math. 18 (1975), 148-181. Zbl0312.12022
  4. [4] Lbekkouri, A., On the construction of normal wildly ramified over Qp, (p = 2), Arch. Math. (Basel) 93 (2009), 331-344.[Crossref][WoS] Zbl1233.11123
  5. [5] Ribes, L., Zalesskii, P., Profinite Groups, Springer-Verlag, Berlin, 2000. Zbl0949.20017
  6. [6] Rotman, J. J., An Introduction to the Theory of Group, Springer-Verlag, New York, 1995. Zbl0810.20001
  7. [7] Serre, J.-P., Local Fields, Springer-Verlag, New York-Berlin, 1979. 
  8. [8] Zariski, O., Samuel, P., Commutative Algebra. Volume II, Springer-Verlag, New York- Heidelberg, 1975. Zbl0313.13001
  9. [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. 

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