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Let k be a complete field under a discrete valuation with residue field k of characteristic p ~ 0. In this paper we shall state a theory of unramified abelian extensions of k (see the main theorem below) and apply this result to fully ramified Zp-extensions of k (see § 4, Theorem 4, Remarks 1 and 2). The main result of this paper is as follows. Fix a fully ramified cyclic extension k' of k of degree m, and for a finite unramified extension K of k, put

journal of the mathematical society of japan

On unramified abelian extensions of a complete field under a discrete valuation with arbitrary residue field of characteristic P≠0 and its application to wildly ramified Zp-extensions