Capitulation des classes logarithmiques et étude de certaines tours de corps de nombres

Abstract : We present the foundations of logarithmic arithmetic and prove results about capitulation of logarithmic class, particularly a logarithmic version of Hilbert?s Theorem 94. We also give an algorithm to compute the kernel of the logarithmic capitulation. In the same view of principalization for logarithmic divisors, we obtain conditions for both finitude and infinitude of the locally cyclotomic tower constructed by Jean-François Jaulent and Florence Soriano-Gafiuk. The theorems shows the fundamental part of logarithmic ramification opposed to the phenomenon of principalization. We investigate a generalization of the locally cyclotomic tower and give a characterization for the finitude
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Christophe Brighi. Capitulation des classes logarithmiques et étude de certaines tours de corps de nombres. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2007. Français. ⟨NNT : 2007METZ016S⟩. ⟨tel-01749002⟩

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