Osaka Journal of Mathematics

On the Isomorphism classes of Iwasawa modules with $\lambda = 3$ and $\mu = 0$

Kazuaki Murakami

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Abstract

For an odd prime number $p$, we classify the isomorphism classes of finitely generated torsion $\Lambda=\mathbb{Z}_{p}[[T]]$-modules with $\lambda=3$ and $\mu=0$, which are free over $\mathbb{Z}_{p}$. We apply this classification to the Iwasawa module associated to the cyclotomic $\mathbb{Z}_{p}$-extension of an imaginary quadratic field.

Article information

Source
Osaka J. Math., Volume 51, Number 4 (2014), 829-867.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1414761903

Mathematical Reviews number (MathSciNet)
MR3273869

Zentralblatt MATH identifier
1319.11074

Subjects
Primary: 11R23: Iwasawa theory 11R29: Class numbers, class groups, discriminants 13C05: Structure, classification theorems

Citation

Murakami, Kazuaki. On the Isomorphism classes of Iwasawa modules with $\lambda = 3$ and $\mu = 0$. Osaka J. Math. 51 (2014), no. 4, 829--867. https://projecteuclid.org/euclid.ojm/1414761903


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