On the classical main conjecture for imaginary quadratic fields

Stéphane Viguié

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arXiv · 1103.1125

On the classical main conjecture for imaginary quadratic fields

Stéphane Viguié

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Abstract

Let p be a prime number which is split in an imaginary quadratic field k. Let \mathfrak{p} be a place of k above p. Let k_\infty be the unique Z_p-extension of k which unramified outside of \mathfrak{p}, and let K_\intfy be a finite extension of k_\infty, abelian over k. In case p \notin {2,3}, we prove that the characteristic ideal of the projective limit of global units modulo elliptic units coincides with the characteristic ideal of the projective limit of the p-class groups. Our approach uses Euler systems, which were first used in this context by K.Rubin. If p \in {2,3}, we obtain a divisibility relation, up to a certain constant.

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Stéphane Viguié. 2011-04-20. On the classical main conjecture for imaginary quadratic fields. https://arxiv.org/abs/1103.1125

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