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Generalized ambiguous logarithmic classes. (Classes logarithmiques generalisées ambiges.) (French) Zbl 0953.11035
For a number field \(k\) and a fixed prime \(l\), the \(l\)-group of logarithmic classes \(\widetilde{Cl}_k\) has been defined by J.-F. Jaulent in [J. Théor. Nombres Bordeux 6, 301-325 (1994; Zbl 0827.11064)]. In this note, given a cyclic \(l\)-extension \(K/k\), with \(G= \text{Gal} (K/k)\), the author considers quotients of \(\widetilde{Cl}_k\) by sub-\(G\)-modules \(\widetilde{\mathcal H}_k\) and proves a formula for the order of \((\widetilde{Cl}_k/ \widetilde{\mathcal H}_k)^G\) in the style of genus theory.

MSC:
11R37 Class field theory
11R23 Iwasawa theory
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