A heuristic for boundedness of ranks of elliptic curves
Name
bounded-ranks.pdf
Description
Accepted version
Size
706.04 KB
Format
Adobe PDF
Checksum (MD5)
f6521a16caf0a4b697c012af103625e3
Author(s)
Park, Jennifer
Poonen, Bjorn
Voight, John
Wood, Melanie Matchett
Date Issued
May 2019
Journal
Journal of the European Mathematical Society
Publisher
European Mathematical Society Publishing House
Citation
Park, Jennifer, et al. “A Heuristic for Boundedness of Ranks of Elliptic Curves.” Journal of the European Mathematical Society 21, 9 (May 2019): 2859–903.
Version
Author's final manuscript
Abstract
We present a heuristic that suggests that ranks of elliptic curves E over Q are bounded. In fact, it suggests that there are only finitely many E of rank greater than 21. Our heuristic is based on modeling the ranks and Shafarevich-Tate groups of elliptic curves simultaneously, and relies on a theorem counting alternating integer matrices of specified rank. We also discuss analogues for elliptic curves over other global fields. Keywords: Elliptic curve; rank; Shafarevich–Tate group
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4171/jems/893
