Euler system for Galois deformations

Ochiai, Tadashi

doi:10.5802/aif.2091

Euler system for Galois deformations
[Système d'Euler pour les déformations galoisiennes]

Ochiai, Tadashi ¹

¹ Osaka University, Department of Mathematics, 1-16 Machikaneyama, Toyonaka, Osaka 560-0043 (Japon)

Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 113-146.

Résumé
Abstract

Dans cet article, on obtient la généralisation de la théorie du système d’Euler pour les déformations galoisiennes. Si on applique ce résultat aux système d’Euler de Beilinson- Kato, on prouve une des inégalités prévues par la conjecture principale d’Iwasawa à deux variables. La clef de notre démonstration est l’utilisation de spécialisations non- arithmétiques. Notre méthode donne une nouvelle preuve plus simple de l’inégalité entre l’idéal caractéristique du groupe de Selmer d’une déformation galosienne et l’idéal associé à un système d’Euler, y compris dans le cas des $ℤ$ -extensions déjà traité par Kato, Perrin-Riou, Rubin.

In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation and the ideal associated to a Euler system even in the case of $ℤ^{d_{p}}$ -extensions already treated by Kato, Perrin-Riou, Rubin.

MR Zbl

DOI : 10.5802/aif.2091

Classification : 11G40, 11R23, 11R34, 11F80, 11F33
Keywords: Euler system, Hida theory, Iwasawa Main conjecture
Mot clés : système d'Euler, théorie de Hida, conjecture principale d'Iwasawa

Affiliations des auteurs :

Ochiai, Tadashi ¹

¹ Osaka University, Department of Mathematics, 1-16 Machikaneyama, Toyonaka, Osaka 560-0043 (Japon)

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Ochiai, Tadashi. Euler system for Galois deformations. Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 113-146. doi : 10.5802/aif.2091. https://aif.centre-mersenne.org/articles/10.5802/aif.2091/

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