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Lbekkouri, Akram

Local extensions with imperfect residue field. (English) Zbl 1443.11244

Ural Math. J. 5, No. 2, 31-54 (2019).
Summary: 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.

MSC:

11S15 Ramification and extension theory
11S20 Galois theory
12F05 Algebraic field extensions

Keywords:

inertia group; Abhyankar’s lemma; imperfect residue field; weakly unramified; solvability; monogenity
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