Arithmétique des courbes elliptiques a réduction supersinguliere en p

2001/09/04 by Bernadette Perrin-Riou, Perrin-Riou, Bernadette
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0109227

openalex publication_date 2001/09/04 · arxiv created 2001/09/05 · arxiv updated 2016/09/07 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

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 λ-invariant and of μ- 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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