Abstract
In this paper the characteristic of the Abelian p-extensions of a field is given using valuations from its cyclotomic extensions. On the basis of this the character group of the Galois groups of the maximal Abelian p-extension of an absolutely unramified complete field is calculated. The results are applied to the case of a two-dimensional local field.
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References
S. V. Vostokov and I. B. Zhukov, “Abelian semiramified extensions of a multidimensional local field,” Rings and Modules. Limit Theorems of Probability Theory [in Russian], 2nd ed., Izdat. Leningrad. Univ., Leningrad (1989).
H. Koch, The Galois Theory of p-Extensions [Russian translation], Moscow (1973).
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E. Witt, “Zyklische Körper und Algebren der Charakteristik p vom Grad pn,” J. Reine Angew. Math.,176, 126–140 (1936).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 80–90, 1991.
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Zhukov, I.B. Abelian p-extensions of an absolutely unramified field. J Math Sci 63, 656–663 (1993). https://doi.org/10.1007/BF01097978
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DOI: https://doi.org/10.1007/BF01097978