6 problems

A rational map is a holomorphic map $f \colon \widehat{\mathbb{C}} \rightarrow \widehat{\mathbb{C}}$ of degree at least $2$; its multipliers are the derivatives associated with its…

Let $k$ be a positive integer with $6\nmid k$, let $E/\mathbb{Q}$ be an elliptic curve, and let $L_k$ be the $k$-th Lattès map attached to $E$. A rational function is arithmeticall…

Let $k$ be a positive integer, let $E/\mathbb{Q}$ be an elliptic curve, and let $L_k$ be the $k$-th Lattès map attached to $E$. A rational function is arithmetically exceptional if…

Let $f$ be a Lattès map on ${\mathbb P^2}$. Lattès-map bifurcation accumulation conjecture. The map $f$ belongs to the closure of the interior of the bifurcation locus. This is pre…

Let $f$ and $g$ be rational functions defining a variable-separated correspondence on $\mathbb{P}^1$. A family of such correspondences is non-isotrivial if it does not become const…

Backward orbit integrality conjecture. If $Q\in\mathbb P^1(\overline K)$ is not $\phi$-preperiodic, then $\phi^-(P)$ contains at most finitely many points in…