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Sur la constante de Kummer-Leopoldt d’un corps de nombres

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Abstract.

Kummer’s lemma for the cyclotomic field gives sufficient local conditions for a unit to be a global p-th power, and can thus be viewed as an early version of Leopoldt’s conjecture. To study generalizations and converse statements, we introduce the ‘‘Kummer-Leopoldt constant’’ κ(F) of a number field F and compute it in Iwasawa theoretic terms. The vanishing of κ(F) gives the desired generalization and converse of Kummer’s lemma.

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Authors and Affiliations

  1. Université Moulay Ismail, Département de Mathématiques et Informatique, B.P 4010 Beni M’hamed, Meknès, Maroc

    Jilali Assim

  2. Université de Franche-Comté, UMR 6623, 16, route de Gray, 25030, Besançon cedex, France

    Thong Nguyen Quang Do

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  1. Jilali Assim
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  2. Thong Nguyen Quang Do
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Correspondence to Jilali Assim.

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Mathematics Subject Classification(2000): Primary 11R23

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Assim, J., Quang Do, T. Sur la constante de Kummer-Leopoldt d’un corps de nombres. manuscripta math. 115, 55–72 (2004). https://doi.org/10.1007/s00229-004-0482-9

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  • DOI: https://doi.org/10.1007/s00229-004-0482-9

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