- Abstract:
- The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
-
(pdf, 411.2KB)
-
- Publisher copy:
- 10.1112/S0010437X19007243
-
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- Publisher:
- Foundation Compositio Mathematica Publisher's website
- Journal:
- Compositio Mathematica Journal website
- Volume:
- 155
- Issue:
- 6
- Pages:
- 1057-1075
- Publication date:
- 2019-05-14
- Acceptance date:
- 2019-01-24
- DOI:
- EISSN:
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1570-5846
- ISSN:
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0010-437X
- Pubs id:
-
pubs:983813
- URN:
-
uri:197c48e8-486b-4680-87ac-8dd1b4ddf108
- UUID:
-
uuid:197c48e8-486b-4680-87ac-8dd1b4ddf108
- Local pid:
- pubs:983813
- Copyright holder:
- Balakrishnan et al.
- Copyright date:
- 2019
- Notes:
- © The Authors 2019. This is the accepted manuscript version of the article. The final version is available online from Foundation Compositio Mathematica at: https://doi.org/10.1112/S0010437X19007243
Journal article
An effective Chabauty-Kim theorem
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