The local Kronecker-Weber theorem
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- by Jonathan Lubin PDF
- Trans. Amer. Math. Soc. 267 (1981), 133-138 Request permission
Abstract:
The extension of a local field generated by adjoining the torsion points on a suitable formal group is essentially the maximal abelian extension of the field. This fact is proven by appealing to the functorial properties of the Herbrand transition function of higher ramification theory.References
- Benedict H. Gross, Ramification in $p$-adic Lie extensions, Journées de Géométrie Algébrique de Rennes (Rennes, 1978) Astérisque, vol. 65, Soc. Math. France, Paris, 1979, pp. 81–102. MR 563473
- Jonathan Lubin and John Tate, Formal complex multiplication in local fields, Ann. of Math. (2) 81 (1965), 380–387. MR 172878, DOI 10.2307/1970622
- Jean-Pierre Serre, Corps locaux, Publications de l’Institut de Mathématique de l’Université de Nancago, VIII, Hermann, Paris, 1962 (French). Actualités Sci. Indust., No. 1296. MR 0150130
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 267 (1981), 133-138
- MSC: Primary 12B10
- DOI: https://doi.org/10.1090/S0002-9947-1981-0621978-X
- MathSciNet review: 621978