Modeling the distribution of ranks, Selmer groups, and Shafarevich–Tate groups of elliptic curves

Using maximal isotropic submodules in a quadratic module over Z[subscript p], we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short exact sequences of cofinite type Z[superscript p]-modules, and then conjecture that as E varies over elliptic...

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Bibliographic Details
Main Authors: Bhargava, Manjul, Kane, Daniel M., Lenstra, Hendrik W., Poonen, Bjorn, Rains, Eric
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:en_US
Published: International Press of Boston 2017
Online Access:http://hdl.handle.net/1721.1/106360
https://orcid.org/0000-0002-8593-2792