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On the Iwasawa $\lambda$-invariants of real abelian fields


Author: Takae Tsuji
Journal: Trans. Amer. Math. Soc. 355 (2003), 3699-3714
MSC (2000): Primary 11R23
DOI: https://doi.org/10.1090/S0002-9947-03-03357-9
Published electronically: May 29, 2003
MathSciNet review: 1990169
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Abstract: For a prime number $p$ and a number field $k$, let $A_\infty$ denote the projective limit of the $p$-parts of the ideal class groups of the intermediate fields of the cyclotomic $\mathbb{Z} _p$-extension over $k$. It is conjectured that $A_\infty$ is finite if $k$ is totally real. When $p$ is an odd prime and $k$ is a real abelian field, we give a criterion for the conjecture, which is a generalization of results of Ichimura and Sumida. Furthermore, in a special case where $p$ divides the degree of $k$, we also obtain a rather simple criterion.


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Additional Information

Takae Tsuji
Affiliation: Department of Mathematics, Tokai University, Hiratsuka, Kanagawa, 259-1292, Japan
Email: tsuji@sm.u-tokai.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-03-03357-9
Keywords: Iwasawa theory, Greenberg's conjecture, abelian fields
Received by editor(s): October 27, 2002
Published electronically: May 29, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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