Selmer groups are intersections of two direct summands of the adelic cohomology
We give a positive answer to a Conjecture by Manjul Bhargava, Daniel M. Kane, Hendrik W. Lenstra Jr., Bjorn Poonen and Eric 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] ).
Autores: Florence Gillibert, Jean Gillibert, Pierre Gillibert, Gabriele Ranieri,
URL de la publicación: https://arxiv.org/pdf/1802.06145.pdf