Abelian p-extensions of an absolutely unramified field

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.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 80–90, 1991.