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Selmer groups are intersection of two direct summands of the adelic cohomology

Selmer groups are intersection of two direct summands of the adelic cohomology 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Selmer groups are intersection of two direct summands of the adelic cohomology

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References (13)

Publisher
Wiley
Copyright
© 2019 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12274
Publisher site
See Article on Publisher Site

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 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.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Oct 1, 2019

Keywords: ;

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