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Bases normales, unités et conjecture faible de leopoldt

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Abstract

Letk be a number field,p an odd prime,R k the ring ofp-integers ofk. We use Iwasawa theory to study theZ p -moduleG(R k ,Z p ) (resp.NB (R k ,Z p )) ofclasses ofZ p -extensions (resp.Z p -extensions having a normal basis overR k ) ofR k . The rank ofG(G k ,Z p ) (resp.NB(R k ,Z p )) is related to Leopoldt's conjecture (resp. weak Leopoldt's conjecture) fork andp.

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  1. Laboratoire de Mathématiques Faculté des Sciences de Basançon, U. A. 741 du C.N.R.S., F25030, Besançon Cedex

    V. Fleckinger & T. Nguyen Quang Do

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  1. V. Fleckinger
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  2. T. Nguyen Quang Do
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Fleckinger, V., Nguyen Quang Do, T. Bases normales, unités et conjecture faible de leopoldt. Manuscripta Math 71, 183–195 (1991). https://doi.org/10.1007/BF02568401

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