Dynamics of quadratic polynomials and rational points on a curve of genus $4$

Hang Fu, Michael Stoll

Let $f_t(z)=z^2+t$. For any $z\in \mathbb{Q}$, let $S_z$ be the collection of $t\in \mathbb{Q}$ such that $z$ is preperiodic for $f_t$. In this article, assuming a well-known conject…