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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 nth Selmer group of E is the intersection of two direct summands of the adelic cohomology group H1(A,E[n]). We also give examples of elliptic curves for which the conclusion of this conjecture does not hold.
Bulletin of the London Mathematical Society – Wiley
Published: Oct 1, 2019
Keywords: ;
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