Normes d'idéaux dans la tour cyclotomique et conjecture de greenberg : hypothèses p-adiques sur les normes d'idéaux

Abstract : Let k be a totally real number field and let k_∞ be its cyclotomic Z_p-extension for p totally split in k. This text completes our article entitled: ``Approche p-adique de la conjecture de Greenberg pour les corps totalement r\'eels'' (Annales Mathématiques Blaise Pascal 2017), by means of heuristics on the p-adic behavior of the norms, in k_n/k, of the ideals of k_n (nth stage of k_∞): an assumption of distribution of these norms should ensure that the algorithms of filtration of the p-class groups of the k_n are uniformly bounded (i.e., lambda=mu=0). Several statistics and numerical examples in the quadratic case confirm the probable exactness of such properties.
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Submitted on : Tuesday, September 19, 2017 - 3:25:07 PM
Last modification on : Saturday, October 6, 2018 - 1:02:10 AM

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  • HAL Id : hal-01546656, version 2
  • ARXIV : 1706.08784

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Georges Gras. Normes d'idéaux dans la tour cyclotomique et conjecture de greenberg : hypothèses p-adiques sur les normes d'idéaux. Completes with numerical computations our previous paper on Greenberg's conjecture. 2017. 〈hal-01546656v2〉

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