The theory of Kolyvagin systems for p=3
Ryotaro Sakamoto1
1 Department of Mathematics University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305-8571, Japan
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 919-946.

Dans cet article, nous considérons la théorie des systèmes de Kolyvagin lorsque p=3 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 p=3.

In this paper, we consider the theory of Kolyvagin systems when p=3 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 p=3.

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Révisé le :
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DOI : 10.5802/jtnb.1300
Classification : 11R23, 11G05, 11R34, 11S25
Mots-clés : Kolyvagin systems, modular symbols, Kurihara conjecture

Ryotaro Sakamoto 1

1 Department of Mathematics University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305-8571, Japan
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ryotaro Sakamoto. The theory of Kolyvagin systems for $p=3$. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 919-946. doi : 10.5802/jtnb.1300. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1300/

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