On the trace map between absolutely abelian number fields of equal conductor

Details On the trace map between absolutely abelian number fields of equal conductor On the trace map between absolutely abelian number fields of equal conductor

2005-05-17

arxiv.org/abs/math/0505348v2

Mathematics

Number Theory

11 pages, 1 figure, uses xypic and amscd. Completely revised version. To appear in Acta Arithmetica

Scientific paper

Let L/K be an extension of absolutely abelian number fields of equal conductor, n. The image of the ring of integers of L under the trace map from L to K is an ideal in the ring of integers in K. We compute the absolute norm of this ideal exactly for any such L/K, thereby sharpening an earlier result of Kurt Girstmair. Furthermore, we define an "adjusted trace map" that allows the proof of Leopoldt's Theorem to be reduced to the cyclotomic case.

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