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- Title
A complete parametrization of cyclic field extensions of 2-power degree.
- Authors
Martinais, Dominique; Schneps, Leila
- Abstract
Let q be a power of 2 at least equal to 8 and ζ be a primitive q-th root of unity, and let K be any field of characteristic zero. We define the group of special projective conorms S as a quotient of the group of elements of K(ζ) of norm 1: S is obviously trival if the groul Gal ( K(ζ)/ K) is cyclic. We prove that for some fields K, the group S is finite, and it is even trivial for certain fields such as ℚ or ℚ( X ,..., X ). We then prove that the group S completely paramatrizes the cycle extensions of K of degree q. We exhibit an explicit polynomial defined over ℚ( T ,..., T ) which parametrizes all cyclic extensions of K of degree q associated to the trivial element of S . In particular, this polynomial parametrizes all cyclic extensions of K of degree q whenever the group S is trivial.
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p181
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026545