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Etage initial d'une ℤ-extension

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Abstract

For a number fieldF that contains ζℓ a ℓth root of unity (ℓ is a prime number), we determine thex such thatF\((\sqrt[\ell ]{x})\) can be embedded in a ℤℓ-extension. We approach the corresponding Kummer radical with the notion of being locally everywhere embedded in a ℤℓ-extension. An idelic description of Galois group is appropriate especially as we utilize the ℓ-adic group of idele of [15]. The illustration concerns ℓ=3 and biquadratic field ℚ\((\zeta _3 ,\sqrt d )\). We detail the step of the calculus and fournish numerical tables.

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  1. Centre de recherche en mathématiques de Bordeaux, 351, cours de la Libération, F-33405, Talence cedex

    Hervé Thomas

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  1. Hervé Thomas
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Thomas, H. Etage initial d'une ℤ-extension. Manuscripta Math 81, 413–435 (1993). https://doi.org/10.1007/BF02567867

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  • DOI: https://doi.org/10.1007/BF02567867

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