On the theory of Kolyvagin systems of rank 0
Sakamoto, Ryotaro1
1 Department of Mathematics Faculty of Science and Technology Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama, 223-8522, Japan
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1077-1102.

In this paper, we define a Kolyvagin system of rank 0 and develop the theory of Kolyvagin systems of rank 0. In particular, we prove that the module of Kolyvagin systems of rank 0 is free of rank one under standard assumptions.

Dans cet article, nous définissons un système Kolyvagin de rang 0 et développons la théorie des systèmes Kolyvagin de rang 0. En particulier, nous prouvons que le module des systèmes Kolyvagin de rang 0 est libre de rang un sous les hypothèses standard.

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DOI: 10.5802/jtnb.1189
Classification: 11F80, 11R34, 11R23
Mots-clés : Kolyvagin system, Selmer group
Sakamoto, Ryotaro 1

1 Department of Mathematics Faculty of Science and Technology Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama, 223-8522, Japan 
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Sakamoto, Ryotaro. On the theory of Kolyvagin systems of rank $0$. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1077-1102. doi : 10.5802/jtnb.1189. http://archive.numdam.org/articles/10.5802/jtnb.1189/

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