Bounds on the Chabauty–Kim Locus of Hyperbolic Curves
Bounds on the Chabauty–Kim Locus of Hyperbolic Curves
Abstract 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 $X/{\mathbb{Q}}$ of genus $g\geq 2$ in terms of $p$, $g$, the Mordell–Weil rank $r$ of …