Bounds on the Chabauty--Kim Locus of Hyperbolic Curves

L. Alexander Betts, David Corwin, Marius Leonhardt

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 rati…