8 problems

Let $S$ be an irreducible algebraic variety with a non-trivial bi-algebraic structure. Let $U\subset \widetilde{S^{\mathrm{an}}}\times S^{\mathrm{an}}$ be an algebraic subvariety f…

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.

Zilber–Pink equality prediction. In the density theorem's description of these Hodge-locus points, the inclusion $\mathbf{MT}(\mathbb{V}_s)\subset g\mathbf{H}g^{-1}$ should be repl…

Let $n$ be a positive integer. For coordinate projections $\mathrm{Pr}_{\mathbf{i}}$ onto any selected $\ell$ pairs of coordinates, call an algebraic set…

Let $f_1,\ldots,f_n$ be holomorphic functions satisfying, for every distinct $i,j\in\{1,\ldots,n\}$, $f_i\notin\mathbb{Q}f_j+\mathbb{C}$. Write $\mathbf{f}=(f_1,\ldots,f_n)$ and…

Let $X$ be a smooth connected algebraic variety over $\mathbb{C}$, with base point $b \in X(\mathbb{C})$. Let $\mathscr{H}_{\mathbb{Z}}$ be a $\mathbb{Z}$-variation of mixed Hodge…

Let $\Omega$ be a bounded symmetric domain, let $\Gamma\subset {\rm Aut}(\Omega)$ be a torsion-free arithmetic lattice, and let … be the uniformization map. For an algebraic subset…

Let $(S,\mathbb{V})$ be a $\mathbb{Z}$VMHS and let $Y\subset\widetilde S$ be an algebraic subvariety. Ax–Lindemann for $\mathbb{Z}$VMHS. The Zariski closure … is a bi-algebraic sub…