Selmer groups are intersection of two direct summands of the adelic cohomology. Issue 5 (24th July 2019)

• Record Type: Journal Article
• Authors: Gillibert, Florence; Gillibert, Jean; Gillibert, Pierre; Ranieri, Gabriele
• Is Part Of: Bulletin of the London Mathematical Society. Volume 51:Issue 5(2019)
• Page Start: 776
• Page End: 786
• Publication Date: 2019-07-24
• Subjects: 11G05 (primary) -- 14G25 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12274
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We give a positive answer to a conjecture by Bhargava, Kane, Lenstra Jr., Poonen and Rains, concerning the cohomology of torsion subgroups of elliptic curves over global fields. This implies that, given a global field k and an integer n, for 100 % of elliptic curves E defined over k, the n th Selmer group of E is the intersection of two direct summands of the adelic cohomology group H 1 ( A, E [ n ] ) . We also give examples of elliptic curves for which the conclusion of this conjecture does not hold.