In this paper, we consider the theory of Kolyvagin systems when and show that this theory still works in a certain setting that has been excluded in previous studies. As an application of this result, we prove a conjecture of Kurihara concerning modular symbols in the case .
Dans cet article, nous considérons la théorie des systèmes de Kolyvagin lorsque et montrons que cette théorie fonctionne toujours dans un certain cadre qui a été exclu dans les études précédentes. Comme application de ce résultat, nous prouvons une conjecture de Kurihara concernant les symboles modulaires dans le cas .
Revised:
Accepted:
Published online:
Keywords: Kolyvagin systems, modular symbols, Kurihara conjecture
Ryotaro Sakamoto 1
CC-BY-ND 4.0
@article{JTNB_2024__36_3_919_0,
author = {Ryotaro Sakamoto},
title = {The theory of {Kolyvagin} systems for $p=3$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {919--946},
year = {2024},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {36},
number = {3},
doi = {10.5802/jtnb.1300},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1300/}
}
TY - JOUR AU - Ryotaro Sakamoto TI - The theory of Kolyvagin systems for $p=3$ JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 919 EP - 946 VL - 36 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1300/ DO - 10.5802/jtnb.1300 LA - en ID - JTNB_2024__36_3_919_0 ER -
%0 Journal Article %A Ryotaro Sakamoto %T The theory of Kolyvagin systems for $p=3$ %J Journal de théorie des nombres de Bordeaux %D 2024 %P 919-946 %V 36 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1300/ %R 10.5802/jtnb.1300 %G en %F JTNB_2024__36_3_919_0
Ryotaro Sakamoto. The theory of Kolyvagin systems for $p=3$. Journal de théorie des nombres de Bordeaux, Volume 36 (2024) no. 3, pp. 919-946. doi: 10.5802/jtnb.1300
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