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Arithm\'etique des courbes elliptiques a r\'eduction supersinguliere en p

Bernadette Perrin-Riou
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Abstract

We review the main conjecture for an elliptic curve on $\Q$ having good supersingular reduction at $p$ and give some consequences of it. Then we define the notion of $\lambda$-invariant and of $\mu$- invariant in this situation, generalizing a work of Kurihara and deduce from it the behaviour of the order of the group of Shafarevich-Tate along the cyclotomique $\Z_p$-extension. By examples, we give some arguments which, by allying theorems and numeral calculations, allow to calculate the order of the $p$-primary part of the group of Shafarevich-Tate in not yet known cases (non trivial Shafarevich-Tate group, curves of rank greater than $ 1$).

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BibTeXRIS

Bernadette Perrin-Riou. 2001-09-05. Arithm\'etique des courbes elliptiques a r\'eduction supersinguliere en p. https://arxiv.org/abs/math/0109227

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