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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The local Kronecker-Weber theorem

Author: Jonathan Lubin
Journal: Trans. Amer. Math. Soc. 267 (1981), 133-138
MSC: Primary 12B10
MathSciNet review: 621978
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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 [Enhancements On Off] (What's this?)

  • [1] B. H. Gross, Ramification in $ p$-adic Lie extensions (Proc. Conf. Formal Groups and Crystalline Cohomology, Rennes, 1978), Astérisque 65 (1979), 81-202. MR 563473 (81e:12018)
  • [2] J. Lubin and J. Tate, Formal complex multiplication in local fields, Ann. of Math. (2) 81 (1965), 380-387. MR 0172878 (30:3094)
  • [3] J.-P. Serre, Corps locaux, Actualités Sci. Indust. No. 1296, Hermann, Paris, 1962. MR 0150130 (27:133)

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Article copyright: © Copyright 1981 American Mathematical Society

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