论文标题
chabauty的边界 - 双曲线曲线的KIM轨迹
Bounds on the Chabauty--Kim Locus of Hyperbolic Curves
论文作者
论文摘要
有条件地在泰特（tate-shafarevich and bloch）上 - 凯托（Kato）的猜想，我们给出了$ p $ - 阿迪克·chabauty-kim基因座的大小，以及理性点的数量，平稳的投射曲线$ x/\ x/\ x/\ x/\ mathbb {Q}它的Jacobian和Bad Primes的$ x $的减少类型。这是使用有效的chabauty-kim方法，Coleman和Balakrishnan--Dogra使用Abelian和二次chabauty方法发现的。
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 $g\geq2$ 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, generalising bounds found by Coleman and Balakrishnan--Dogra using the abelian and quadratic Chabauty methods.
