On the Isomorphism Classes of Iwasawa Modules Associated to Imaginary Quadratic Fields with $λ = 2$
Vol. 6 (1999), No. 2, Page 371--396.
Koike, Masanobu
On the Isomorphism Classes of Iwasawa Modules Associated to Imaginary Quadratic Fields with $λ = 2$
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
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 $λ = 2$ and $μ = 0$ 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
Received: 1998-04-01