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This article is cited in 35 scientific papers (total in 35 papers)
On formulae for the class number of real Abelian fields
L. V. Kuz'minab a Russian Research Centre "Kurchatov Institute"
b Information Technologies Institute
Abstract:
For a given real Abelian field $k$ and a given prime natural number $\ell$ we obtain an index formula for the order of the group $\operatorname{Cl}(k)_{\ell,\varphi}$, where $\operatorname{Cl}(k)_{\ell}$ is the $\ell$-component of the class group of $k$ $\operatorname{Cl}(k)_{\ell,\varphi}$ denotes the $\varphi$-component of
$\operatorname{Cl}(k)_\ell$ corresponding to a ${\mathbf Q}_\ell$-irreducible character $\varphi$ of the Galois group $G(k/{\mathbf Q})$ that is trivial on the Sylow
$\ell$-subgroup of $G(k/{\mathbf Q})$. This result generalizes a conjecture of Gras. The proofs rely on the “main conjecture” of Iwasawa theory.
Received: 14.11.1995
Citation:
L. V. Kuz'min, “On formulae for the class number of real Abelian fields”, Izv. RAN. Ser. Mat., 60:4 (1996), 43–110; Izv. Math., 60:4 (1996), 695–761
Linking options:
https://www.mathnet.ru/eng/im79https://doi.org/10.1070/IM1996v060n04ABEH000079 https://www.mathnet.ru/eng/im/v60/i4/p43
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Abstract page: | 378 | Russian version PDF: | 235 | English version PDF: | 27 | References: | 47 | First page: | 1 |
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