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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)

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