Bounds on the Chabauty–Kim Locus of Hyperbolic Curves

L. Alexander Betts, David Corwin, Marius Leonhardt

Research output: Contribution to journalArticlepeer-review


Conditionally on the Tate–Shafarevich and Bloch–Kato Conjectures, we give an explicit upper bound on the size of the p-adic Chabauty–Kim locus, and hence on the number of rational points, of a smooth projective curve X/Q of genus g ≥ 2 in terms of p, g, the Mordell–Weil rank r of its Jacobian, and the reduction types of X at bad primes. This is achieved using the effective Chabauty–Kim method, generalizing bounds found by Coleman and Balakrishnan–Dogra using the abelian and quadratic Chabauty methods.

Original languageAmerican English
Pages (from-to)9705-9727
Number of pages23
JournalInternational Mathematics Research Notices
Issue number12
StatePublished - 1 Jun 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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