Comptes Rendus
Géométrie algébrique
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
[Vérification exacte de la conjecture BSD forte pour certaines variétés abéliennes absolument simples]
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 483-489.

Soit X un des 28 quotients d’Atkin–Lehner d’une courbe X 0 (N) tel que X est de genre 2 et sa jacobienne J est absolument simple. On démontre que le groupe de Shafarevich–Tate Ш(J/) est trivial. Ceci vérifie la conjecture BSD forte pour J.

Let X be one of the 28 Atkin–Lehner quotients of a curve X 0 (N) such that X has genus 2 and its Jacobian variety J is absolutely simple. We show that the Shafarevich–Tate group Ш(J/) is trivial. This verifies the strong BSD conjecture for J.

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DOI : 10.5802/crmath.313
Classification : 11G40, 11-04, 11G10, 11G30, 14G35

Timo Keller 1 ; Michael Stoll 1

1 Lehrstuhl Mathematik II (Computeralgebra), Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Exact verification of the strong {BSD} conjecture for some absolutely simple abelian surfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {483--489},
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     doi = {10.5802/crmath.313},
     language = {en},
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Timo Keller; Michael Stoll. Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 483-489. doi : 10.5802/crmath.313. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.313/

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