Chromatic Selmer groups and arithmetic invariants of elliptic curves

Ito Sprung, Florian¹

¹ School of Mathematical and Statistical Sciences Arizona State University Tempe, AZ 85287-1804, USA

Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 3.2, pp. 1103-1114.

Abstract (VO)

Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes $p$. We sketch their role in establishing the $p$-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the ${\mathbb{Z}}_p^2$-extension of a quadratic imaginary number field in which $p$ splits in Section 6.

Résumé

Les groupes de Selmer chromatiques sont des modifications des groupes de Selmer, qui contiennent des informations locales pour les nombres premiers $p$ supersinguliers. Dans les sections 2–5, on esquisse leur rôle dans la démonstration de la partie $p$-primaire de la formule de Birch et Swinnerton-Dyer, et ensuite, dans la section 6, on étudie la croissance du rang de Mordell–Weil le long de la ${\mathbb{Z}}_p^2$-extension d’un corps quadratique imaginaire dans lequel $p$ est décomposé.

Détail

Reçu le : 2019-12-12
Révisé le : 2020-06-09
Accepté le : 2020-07-28
Publié le : 2022-01-26

DOI : 10.5802/jtnb.1190

Classification : 11G40, 11R23, 14H52
Keywords: Elliptic curves, Selmer group, Mordell–Weil rank

Licence : CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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