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Higher local class field theory

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WAN, SHIYUAN
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LOCAL CLASS FIELD THEORY: PERFECT RESIDUE FIELD CASE

Russian Academy of Sciences. Izvestiya Mathematics, 1994
Let \(F\) be a complete discrete valued field with perfect residue field of characteristic \(p>0\). A class field theory for the most interesting abelian extension of \(F\), the fully ramified \(p\)-extension was given by \textit{M. Hazewinkel} [Corps de classes local, Appendix to \textit{M. Demazure} and \textit{P.
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EXPLICIT CONSTRUCTION OF CLASS FIELD THEORY FOR A MULTIDIMENSIONAL LOCAL FIELD

Mathematics of the USSR-Izvestiya, 1986
Let \(F\) be an \(n\)-dimensional local field, \(F^{ab}\) be the maximal abelian extension of \(F\) and \(K^M_n(F)\) be Milnor's \(K\)-functor. By higher class field theory there exists a canonical homomorphism \(\psi: K^M_n(F)\to \mathrm{Gal}(F^{ab}/F)\).
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The Nottingham group and local class field theory

Journal of the London Mathematical Society, 2009
Let Fq be the algebraic closure of the finite field Fq. Let G be the group of continuous Fq-automorphisms Ð of the abelian closure of the series field Fq((t)) such that Ð(t) ¸ tFq[[t]] ~ . The set Fq[[t]] ~ is a group for the non-commutative Ore multiplication of the series (the ordinary multiplication twisted by the Frobenius map). In this paper,
Laubie, François, Moioli, Olivier
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Local class field theory. I

1985
L'article est la première partie d'une ouvrage qui a comme but un exposé detailé du mémoire de \textit{M. Hazewinkel}: ''Local class field theory is easy'', Adv. Math. 18, 148--181 (1975; Zbl 0312.12022).
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Local class field theory

1984
By a local field in commutative algebra we mean usually a field of fractions of a complete discrete valuation ring. This notion has many applications in arithmetics and algebraic geometry. In the papers [Usp. Mat. Nauk 30, No. 1 (181), 253--254 (1975; Zbl 0302.14005); Izv. Akad. Nauk SSSR, Ser. Mat.
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The Existence Theorem and Local Class Field Theory

1986
We must prove that any open subgroup H of J k containing k* belongs to some abelian extension. Thus at some point, we have to start exhibiting abelian extensions of k. There are not that many ways of doing this. One general way is to make cyclotomic extensions, and when the n-th roots of unity are in k, to make Kummer extensions, i.e.
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A Generalization of Local Class Field Theory

American Journal of Mathematics, 1938
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Local class field theory

2022
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Local Class Field Theory

Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen Mit Besonderer Berücksichtigung Der Anwendungsgebiete, 1999
Jürgen Neukirch
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