Some results on local fields

Akram Lbekkouri

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2013)

  • Volume: 67, Issue: 2
  • ISSN: 0365-1029

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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 67.2 (2013): null. <http://eudml.org/doc/289811>.

@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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Local fields; local number fields; Wild ramification; intermediate extension; standard p-over-extensions; semi-direct product; inertia group.},
language = {eng},
number = {2},
pages = {null},
title = {Some results on local fields},
url = {http://eudml.org/doc/289811},
volume = {67},
year = {2013},
}

TY - JOUR
AU - Akram Lbekkouri
TI - Some results on local fields
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2013
VL - 67
IS - 2
SP - null
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.
UR - http://eudml.org/doc/289811
ER -

References

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  1. Abbes, A., Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (5) (2002), 879–920. 
  2. Artin, E., Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1942. 
  3. Hazewinkel, M., Local class field theory is easy, Adv. Math. 18 (1975), 148–181. 
  4. Lbekkouri, A., On the construction of normal wildly ramified over ℚ p , ( p ≠ 2 ), Arch. Math. (Basel) 93 (2009), 331–344. 
  5. Ribes, L., Zalesskii, P., Profinite Groups, Springer-Verlag, Berlin, 2000. 
  6. Rotman, J. J., An Introduction to the Theory of Group, Springer-Verlag, New York, 1995. 
  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. 
  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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