Logarithmic classes in the narrow sense. (Classes logarithmiques au sens restreint.) (French) Zbl 0887.11044

Let \(\ell\) be a prime. The concept of the logarithmic \(\ell\)-class group \(\widetilde{{\mathcal C}\ell}_K\) of a number field \(K\) has been introduced by J.-F. Jaulent [J. Théor. Nombres Bordx. 6, 301-325 (1994; Zbl 0827.11064)]. It has its origin in studies of some \(\ell\)-extensions in connection with \(K\)-theory. A conjecture of Gross asserts that \(\widetilde{{\mathcal C}\ell}_K\) is finite. Take \(\ell=2\). The author introduces the concept of the logarithmic 2-class group in the narrow sense and investigates its properties. One of the main results is a formula for the ambiguous logarithmic classes in the case of a cyclic 2-extension \(L/K\) assuming that the finiteness conjecture is true.
Reviewer: V.Ennola (Turku)


11R23 Iwasawa theory
11R70 \(K\)-theory of global fields


Zbl 0827.11064
Full Text: DOI EuDML


[1] F. DIAZ Y DIAZ & F. SORIANO,Approche algorithmique du groupe des classes logarithmiques, soumis à J. Numb. Th.. · Zbl 0930.11079
[2] G. GRAS,Classes généralisées invariantes, J. Math. Soc. Japon3 (1994), 467–476. · Zbl 0816.11057
[3] J.-F. JAULENT,L’arithmétique des l-extensions (Thèse), Publ. Math. Fac. Sci. Besançon, Théor. Nombres 1984/1985, 1985/1986 (1986), 1–348.
[4] J.-F. JAULENT,Noyau Universel et Valeurs absolues, Journées Arithmétiques de Marseille-Luminy, Astérisque 198-199-200 (1991), 187–207.
[5] J.-F. JAULENT,Sur le noyau sauvage des corps de nombres, Acta Arithmetica LXVII.4 (1994), 335–348.
[6] J.-F. JAULENT,Classes logarithmiques des corps de nombres, J. Théor. Nombres Bordeaux.6 (1994), 303–327.
[7] F. SORIANO,Classes logarithmiques ambiges des corps quadratiques, Acta Arithmetica (à paraître). · Zbl 0869.11081
[8] F. SORIANO,Cyclicité du groupe des classes logarithmiques des extensions de type (CM), Prépublication.
[9] F. SORIANO,Classes logarithmiques généralisées ambiges, Prépublication.
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