Determination of Conductors from Galois Module Structure

Details Determination of Conductors from Galois Module Structure Determination of Conductors from Galois Module Structure

2001-10-03

arxiv.org/abs/math/0110048v1

Math. Z. 241 (2002) 227-245

Mathematics

Number Theory

18 pages

Scientific paper

Let F denote an unramified extension of the cyclotomic extension of Q_p by (p^n)th roots of unity, for an odd prime p. We determine the conductors of those Kummer extensions of F of degree dividing p^n 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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