The theory of Kolyvagin systems for $p=3$

Sakamoto, Ryotaro

Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 919-946

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 $p=3$.

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 $p=3$.

Classification : 11R23, 11G05, 11R34, 11S25
Keywords: Kolyvagin systems, modular symbols, Kurihara conjecture

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