On the Iwasawa $\lambda$-invariants of real abelian fields
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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.References
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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
- Received by editor(s): October 27, 2002
- Published electronically: May 29, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 3699-3714
- MSC (2000): Primary 11R23
- DOI: https://doi.org/10.1090/S0002-9947-03-03357-9
- MathSciNet review: 1990169