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

Henri Johnston
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Abstract

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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Henri Johnston. 2006-02-02. On the trace map between absolutely abelian number fields of equal conductor. https://doi.org/10.4064/aa122-1-7

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