11 problems

Let $g\geq 1$ be an integer, let $\pi\colon\mathfrak{A}_g\to\mathbb{A}_g$ be the universal family of principally polarized abelian varieties with suitable level structure, and let…

Let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module of generic characteristic acting diagonally on $\mathbb{G}_a^g$, and let $\{x_k\}$ be a strict sequence of torsion points in…

Real Manin–Mumford conjecture for the Gamma function. Conditional on Conjecture, if $W$ is an irreducible real algebraic curve in $\mathbb R^2$ containing infinitely many Gamma-spe…

Manin–Mumford type conjecture. If an algebraic curve $W\subseteq\mathbb C^2$ contains infinitely many $f$-special points, then $W$ must be $f$-special.

Relative Manin-Mumford conjecture. The stated alternative holds.

Let $G$ be a semi-abelian variety. Define a special subvariety to be a translate of a semi-abelian subvariety of $G$ by a torsion point, and call the zero-dimensional special subva…

Let $S$ be an irreducible variety over $\mathbb{C}$, let $\pi_S\colon\mathcal{A}\rightarrow S$ be an abelian scheme, and let $X$ be a closed irreducible subvariety dominating $S$.…

Let $C$ be an algebraic curve of genus greater than one defined over a number field $K$, together with an embedding defined over $K$ of $C$ into its Jacobian. Then…

Let $\mathcal{A}=(\mathbb{G}_{a}^{m},\Phi)$ be a uniformizable $T$-module of dimension $m>1$ such that there exists $i\in\mathbb{N}\setminus\{0\}$ for which the leading coefficient…

Let $(F,\Phi)$ be an $A$-module and $H ot i F$ a $q$-variety. Let $Gamma={0}$, so that the division hull $overline{Gamma}$ is the torsion subgroup $operatorname{Tor}(F)$. **Denis–M…

Let $f$ be a complex polynomial automorphism of Hénon type of the affine plane, and let $C$ be an irreducible algebraic curve containing infinitely many periodic points of $f$. An…