A heuristic for boundedness of ranks of elliptic curves
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 theor...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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European Mathematical Society Publishing House
2020
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| Online Access: | https://hdl.handle.net/1721.1/124997 |
| _version_ | 1826201658967719936 |
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| author | Park, Jennifer Poonen, Bjorn Voight, John Wood, Melanie Matchett |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Park, Jennifer Poonen, Bjorn Voight, John Wood, Melanie Matchett |
| author_sort | Park, Jennifer |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T11:54:46Z |
| format | Article |
| id | mit-1721.1/124997 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:54:46Z |
| publishDate | 2020 |
| publisher | European Mathematical Society Publishing House |
| record_format | dspace |
| spelling | mit-1721.1/1249972022-10-01T06:55:37Z A heuristic for boundedness of ranks of elliptic curves Park, Jennifer Poonen, Bjorn Voight, John Wood, Melanie Matchett Massachusetts Institute of Technology. Department of Mathematics 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 National Science Foundation (U.S.) (Grant DMS-1069236) National Science Foundation (U.S.) (Grant DMS-1601946) Simons Foundation (Grant 340694) Simons Foundation (Grant 402472) Simons Foundation (Grant 550033) 2020-05-04T17:30:56Z 2020-05-04T17:30:56Z 2019-05 2019-11-18T17:57:52Z Article http://purl.org/eprint/type/JournalArticle 1435-9855 1435-9863 https://hdl.handle.net/1721.1/124997 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. en http://dx.doi.org/10.4171/jems/893 Journal of the European Mathematical Society Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Mathematical Society Publishing House MIT web domain |
| spellingShingle | Park, Jennifer Poonen, Bjorn Voight, John Wood, Melanie Matchett A heuristic for boundedness of ranks of elliptic curves |
| title | A heuristic for boundedness of ranks of elliptic curves |
| title_full | A heuristic for boundedness of ranks of elliptic curves |
| title_fullStr | A heuristic for boundedness of ranks of elliptic curves |
| title_full_unstemmed | A heuristic for boundedness of ranks of elliptic curves |
| title_short | A heuristic for boundedness of ranks of elliptic curves |
| title_sort | heuristic for boundedness of ranks of elliptic curves |
| url | https://hdl.handle.net/1721.1/124997 |
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