Journal article
Explicit Chaubauty–Kim for the split Cartan modular curve of level 13
- Abstract:
- We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in a method to compute a finite set of p-adic points, containing the rational points, on a curve of genus g > 2 over the rationals whose Jacobian has Mordell–Weil rank g and Picard number greater than one, and which satisfies some additional conditions. This is then applied to determine the rational points of the modular curve Xs (13), completing the classification of non-CM elliptic curves over Q with split Cartan level structure due to Bilu–Parent and Bilu–Parent–Rebolledo.
- Publication status:
- Accepted
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 819.3KB, Terms of use)
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- Publisher copy:
- 10.4007/annals.2019.189.3.6
Authors
- Publisher:
- Princeton University, Department of Mathematics
- Journal:
- Annals of Mathematics More from this journal
- Volume:
- 189
- Issue:
- 3
- Pages:
- 885-944
- Publication date:
- 2019-05-14
- Acceptance date:
- 2019-02-20
- DOI:
- ISSN:
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1939-8980
- Keywords:
- Pubs id:
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pubs:983030
- UUID:
-
uuid:2c740bbd-9e12-4d19-acf1-322709461b00
- Local pid:
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pubs:983030
- Source identifiers:
-
983030
- Deposit date:
-
2019-03-15
- ARK identifier:
Terms of use
- Copyright holder:
- Department of Mathematics, Princeton University
- Copyright date:
- 2019
- Notes:
- © Department of Mathematics, Princeton University.This is the accepted manuscript version of the article. The final version is available online from Princeton University, Department of Mathematics at: https://www.jstor.org/stable/10.4007/annals.2019.189.3.6
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