Geodesic
Local extensions with imperfect residue field
Ural mathematical journal, Tome 5 (2019) no. 2, pp. 31-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with some aspects of general local fields and tries to elucidate some obscure facts. Indeed, several questions remain open, in this domain of research, and literature is getting scarce. Broadly speaking, we present a full description of the absolute Galois group in all cases with answers on the solvability, prosolvability and procyclicity. Furthermore, we give a result that makes “some” generalization to Abhyankar’s Lemma in local case. Half-way a short section, containing a view of some future research loosely discussed, presents an attempt in the development of the theory. An Annexe elucidate several important points, concerning Hilbert’s theory.
Keywords: Abhyankar’s Lemma, Imperfect residue field, Weakly unramified, Solvability, Monogenity.
Mots-clés : Inertia group 
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Akram Lbekkouri. Local extensions with imperfect residue field. Ural mathematical journal, Tome 5 (2019) no. 2, pp. 31-54. http://geodesic.mathdoc.fr/item/UMJ_2019_5_2_a3/

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