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 -extensions already treated by Kato, Perrin-Riou, Rubin.
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.
Keywords: Euler system, Hida theory, Iwasawa Main conjecture
Mot 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{\textquoteright}institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2091}, mrnumber = {2141691}, zbl = {02162466}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2091/} }
TY - JOUR AU - Ochiai, Tadashi TI - Euler system for Galois deformations JO - Annales de l'Institut Fourier PY - 2005 SP - 113 EP - 146 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2091/ DO - 10.5802/aif.2091 LA - en ID - AIF_2005__55_1_113_0 ER -
Ochiai, Tadashi. Euler system for Galois deformations. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 113-146. doi : 10.5802/aif.2091. http://archive.numdam.org/articles/10.5802/aif.2091/
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