Euler system for Galois deformations  [ Système d'Euler pour les déformations galoisiennes ]
Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 113-146.

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 -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 d p -extensions already treated by Kato, Perrin-Riou, Rubin.

DOI : https://doi.org/10.5802/aif.2091
Classification : 11G40,  11R23,  11R34,  11F80,  11F33
Mots clés : système d'Euler, théorie de Hida, conjecture principale d'Iwasawa
@article{AIF_2005__55_1_113_0,
     author = {Ochiai, Tadashi},
     title = {Euler system for Galois deformations},
     journal = {Annales de l'Institut Fourier},
     pages = {113--146},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {1},
     year = {2005},
     doi = {10.5802/aif.2091},
     zbl = {02162466},
     mrnumber = {2141691},
     language = {en},
     url = {archive.numdam.org/item/AIF_2005__55_1_113_0/}
}
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. http://archive.numdam.org/item/AIF_2005__55_1_113_0/

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