7 problems

Generalized relative Manin–Mumford conjecture. Under these hypotheses, $Y$ is contained in a proper torsion coset.

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 $A$ be the coefficient ring and let $B$ be a subring of $A$. Let $\mathcal{A}=(\mathbb{G}_{a}^{m},\Phi)$ be an abelian uniformizable $T$-module, meaning an abelian uniformizabl…

Let $C$ be an algebraic curve of genus $g \geq 2$, defined over a number field and embedded in its Jacobian $J$. Manin–Mumford conjecture. The set of torsion points of $J$ which li…

Let $X$ be an algebraic variety over $\mathbb{C}$. Define a special subvariety of $X$ to be a translate by a torsion point of an abelian subvariety when $X$ is an abelian variety,…

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…