Determination of Conductors from Galois Module Structure
Abstract
Let F denote an unramified extension of the cyclotomic extension of Qp by (pn)th roots of unity, for an odd prime p. We determine the conductors of those Kummer extensions of F of degree dividing pn which are Galois over the maximal unramified subfield of F. This follows from a comparison of the Galois module structure of the multiplicative group of F with the unit filtration of F.
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