An effective Chabauty–Kim theorem

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...

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Bibliographic Details
Published inCompositio mathematica Vol. 155; no. 6; pp. 1057 - 1075
Main Authors Balakrishnan, Jennifer S., Dogra, Netan
Format Journal Article
LanguageEnglish
Published London, UK London Mathematical Society 01.06.2019
Cambridge University Press
Subjects
Power
Theorems
New York
curves
effective methods
11D45 (secondary)
rational points
14G05 (primary)
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X19007243