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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
##### Keywords:
logarithmic class in the narrow sense; ambiguous class
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##### References:
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