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On the two-variable Iwasawa main conjecture

Published online by Cambridge University Press:  25 September 2006

Tadashi Ochiai
Tadashi Ochiai
Affiliation:
Department of Mathematics, Osaka University, 1-16, Machikaneyama, Toyonaka, Osaka, Japan, 560-0043 ochiai@math.wani.osaka-u.ac.jp
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Abstract

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This paper is a continuation of the author's previous work, where we studied one of the inequalities between the characteristic ideal of the Selmer group and the ideal of the $p$-adic $L$-function predicted by the two-variable Iwasawa main conjecture for a nearly ordinary Hida deformation $\mathcal{T}$. In this paper, we study several properties of the Selmer group and the $p$-adic $L$-function solving some of the open questions raised in the author's previous work. As applications, we have an infinite family of elliptic cuspforms where the cyclotomic Iwasawa main conjecture holds for every cuspform in the family.

Keywords

Iwasawa main conjectureSelmer group$p$-adic $L$-functionHida theory11F3311F8011G4011R2311R34
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1157 - 1200
Copyright
Foundation Compositio Mathematica 2006