## On the Isomorphism Classes of Iwasawa Modules Associated to Imaginary Quadratic Fields with $Î» = 2$

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 2, Page 371--396.

Koike, Masanobu
On the Isomorphism Classes of Iwasawa Modules Associated to Imaginary Quadratic Fields with $Î» = 2$
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Abstract:
Let $p$ be an odd prime number. Let $\varLambda = \Zp[[T]]$. We determine the $\varLambda$-isomorphism classes of finitely generated $\varLambda$-torsion $\varLambda$-modules with $Î» = 2$ and $Î¼ = 0$ which have no non-trivial finite $\varLambda$-submodule. We apply this classification to Iwasawa modules $X = \varprojlim A_n$ associated to the cyclotomic $\Zp$-extensions of imaginary quadratic fields and give some numerical examples.

Mathematics Subject Classification (1991): 11R23
Mathematical Reviews Number: MR1706948