On standard extensions of local fields

Open access


Let L/K be any separable extension of complete discrete valued fields of degree p. This work, is a study of some "standard over-extensions" of L/K, with the description of their Galois groups. The second target, which is the aim of this work, concerns the Galois closure of L/K. The study of the normal case has been done in some former work.

[1] E. Artin, Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1944, Second edition.

[2] M.Hazewinkel, Local class field theory is easy, Adv. in Math.18 (1975), 148{181.

[3] B. Huppert, Endliche Gruppen I, Grundlehren der mathematischen Wissenschaften Volume 134, 1967

[4] G. James and M. Liebeck, Representations and characters of groups, Cambridge University Press, New York, 2001.

[5] M.Krasner, Sur la primitivite des corps p-adiques, Mathematica Cluj t:13 (1937) pp. 72{191.

[6] M. Krasner, Nombres des extensions de degre donne d'un corps p-adique, Les tendances ge- ometriques en Algebre et en theorie des nombres, Edition du centre national de la recherche scientifique Paris (1966) pp. 143{169.

[7] S. Lang, Algebraic number theory, Addison-Wesley publishing company, INC, 1968.

[8] A. Lbekkouri, On the Ore-Krasner equation, Scientiae Mathematicae Japonicae Vol. 74, No. 2 and 3 Whole Number 268 December 2011 pp. 121{134.

[9] A. Lbekkouri, On the construction of normal wildly ramified extensions over Qp p 6= 2, Archiv der Math.Volume 93, Number 4 (2009), 331{344.

[10] A. Lbekkouri, On the construction of normal wildly ramified extensions over Q2, Archiv der Mathematik Volume 93, Number 3 (2009), 235{243

[11] J. Neukirch, Class Field Theory (Grundlehren DerMathWissenschaften, 1986).

[12] P. Ribenboim, L'Arithmetique des corps Volume 2, Hermann Paris 1972.

[13] L. Ribes and P.Zalesskii, Profinite groups, A series of Modern surveys in Mathematics, Volume 40 Springer 2000.

[14] P. Rotman, An introduction to group theory, Springer Graduate texts in Mathematics, 2010.

[15] I.R. Safarevic, On p-extensions, Amer. Math. Soc. Transl. 4(2) (1954).

[16] J.P. Serre, Une formule de masse pour les extensions totalement ramifiees de degre donne dun corps local, Comptes Rendus 286, 1978, pp. 1031-1036.

[17] J.P. Serre, Local fields, Springer 1979.