On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger

2009/11/01 by Jan Nekovář · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research #Mathematics #Parity (physics) #Conjecture #Elliptic curve #Pure mathematics #Class number #Combinatorics #Mathematics education #Geometry

paper · pdf · doi:10.1112/s0010437x09003959

openalex publication_date 2009/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Abstract We prove the parity conjecture for the ranks of p -power Selmer groups ( p ⁄=2) of a large class of elliptic curves defined over totally real number fields.

Citations

• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
• Finding large Selmer rank via an arithmetic theory of local constants
• Modular Elliptic Curves and Fermat's Last Theorem
• Quelques applications du théorème de densité de Chebotarev

Cited by

• Birch and Swinnerton-Dyer conjecture [wikipedia]