Tohoku Mathematical Journal

The index of elliptic units in $\boldsymbol{Z}_p$-extensions, II

Hassan Oukhaba

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Abstract

In this paper we continue to explore the index of elliptic units. In a previous article we determined the asymptotic behavior in $\boldsymbol{Z}_p$-extensions of the $p$-part of this index divided by the $p$-part of the ideal class number. We proved the existence of an invariant $\mu_\infty$ which governs this behavior, and gave sufficient conditions for the vanishing of $\mu_\infty$. Here we give examples with nonzero $\mu_\infty$, especially in the case of anticyclotomic $\boldsymbol{Z}_p$-extensions.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 2 (2009), 253-265.

Dates
First available in Project Euclid: 24 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1245849447

Digital Object Identifier
doi:10.2748/tmj/1245849447

Mathematical Reviews number (MathSciNet)
MR2541409

Zentralblatt MATH identifier
1231.11066

Subjects
Primary: 11G16: Elliptic and modular units [See also 11R27]
Secondary: 11R23: Iwasawa theory

Citation

Oukhaba, Hassan. The index of elliptic units in $\boldsymbol{Z}_p$-extensions, II. Tohoku Math. J. (2) 61 (2009), no. 2, 253--265. doi:10.2748/tmj/1245849447. https://projecteuclid.org/euclid.tmj/1245849447


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