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2013 On the two-variables main conjecture for extensions of imaginary quadratic fields
Stéphane Vigué
Tohoku Math. J. (2) 65(3): 441-465 (2013). DOI: 10.2748/tmj/1378991025

Abstract

Let $p$ be a prime number at least 5, and let $k$ be an imaginary quadratic number field in which $p$ decomposes into two conjugate primes. Let $k_\infty$ be the unique ${\boldsymbol Z}_p^2$-extension of $k$, and let $K_\infty$ be a finite extension of $k_\infty$, abelian over $k$. We prove that in $K_\infty$, the characteristic ideal of the projective limit of the $p$-class group coincides with the characteristic ideal of the projective limit of units modulo elliptic units. Our approach is based on Euler systems, which were first used in this context by Rubin.

Citation

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Stéphane Vigué. "On the two-variables main conjecture for extensions of imaginary quadratic fields." Tohoku Math. J. (2) 65 (3) 441 - 465, 2013. https://doi.org/10.2748/tmj/1378991025

Information

Published: 2013
First available in Project Euclid: 12 September 2013

MathSciNet: MR3102544
Digital Object Identifier: 10.2748/tmj/1378991025

Subjects:
Primary: 11G16
Secondary: 11R23, 11R65

Rights: Copyright © 2013 Tohoku University

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Vol.65 • No. 3 • 2013
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