Triviality in ideal class groups of Iwasawa-theoretical abelian number fields

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概要

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• Let S be a non-empty finite set of prime numbers and, for each p in S, let \bm{Z}_p denote the ring of p-adic integers. Let F be an abelian extension over the rational field such that the Galois group of F over some subfield of F with finite degree is topologically isomorphic to the additive group of the direct product of \bm{Z}_p for all p in S. We shall prove that each of certain arithmetic progressions contains only finitely many prime numbers l for which the l-class group of F is nontrivial. This result implies our conjecture in \cite{H2} that the set of prime numbers l for which the l-class group of F is trivial has natural density 1 in the set of all prime numbers.

• 社団法人 日本数学会の論文
• 2005-07-01

著者

• Horie Kuniaki

  Department Of Mathematics Tokai University

関連論文

• The ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals
• Certain primary components of the ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals
• The ideal class group of the basic $Z_p$-extension over an imaginary quadratic field
• Primary components of the ideal class group of an Iwasawa-theoretical abelian number field
• Triviality in ideal class groups of Iwasawa-theoretical abelian number fields

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