A monogenic Hasse-Arf theorem

Borger, James

doi:10.5802/jtnb.451

Cited by 5 publications

(3 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Hasse-Arf theorem, Herbrand's Theorem, more generally Sen's theorem, and Hilbert's formula which are true under the strong hypothesis "L/K separable" (see for example [18]); however remain true in the more general case when "L/K is assumed to be monogenic" see [3,20,23,24] for Hasse-Arf theorem.…”

Section: On the Monogenic Case (A Step In The Generalization)mentioning

confidence: 99%

Local Extensions With Imperfect Residue Field

Lbekkouri

2019

UMJ

View full text Add to dashboard Cite

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.

show abstract

Section: On the Monogenic Case (A Step In The Generalization)mentioning

confidence: 99%

Local Extensions With Imperfect Residue Field

Lbekkouri

2019

UMJ

View full text Add to dashboard Cite

show abstract

“…This phenomenon, which does not appear in the classical theory of local fields, is known as ferocious ramification [82], and has been the major source of trouble in developing ramification theory for higher dimensional local fields, or more generally for complete discrete valuation fields with imperfect residue field. Various approaches and contributions to the theory, in chronological order, are due to K. Kato [33,34,35], O. Hyodo [27], I. Fesenko [14], I. Zhukov [81,82], A. Abbes and T. Saito [1] [2], and J. Borger [7,6].…”

Section: Remark 24mentioning

confidence: 99%

An introduction to higher dimensional local fields and adeles

Morrow¹

2012

Preprint

View full text Add to dashboard Cite

show abstract

“…Until Abbes and Saito' work it was a significant open problem to systematically generalise the classical ramification theory for complete discrete valuation fields with perfect residue field to the imperfect residue field situation; some alternative approaches are due to J. Borger [4] [3], K. Kato [13] [14], and I. Zhukov [28] [29]. Geometrically, the importance of this lies in the following situation.…”

Section: Proofmentioning

confidence: 99%