14 problems

Mixed hybrid conjecture. (1) The subvariety $S\subseteq {\mathbb A}_\Gamma$ is weakly special. (2) If, for some $s\in S$, one has $V\cap (A_s)_{\operatorname{tors}}\neq\varnothing$…

Let $X \stackrel{\iota}{\hookrightarrow} {\mathcal S}$ be a closed irreducible algebraic subvariety of a mixed Shimura variety ${\mathcal S}$. Let…

Revised relative unlikely-intersection conjecture. The intersection $Z\cap\mathcal{G}^{[>d]}$ is not Zariski dense in $Z$.

Pink's original relative Manin–Mumford conjecture. The intersection $Z\cap\mathcal{G}^{[>d]}$ is not Zariski dense in $Z$.

Relative Manin-Mumford conjecture. The stated alternative holds.

Let $M$ be a mixed Shimura variety, let $Z\subset M$ be a subvariety, and let $\delta(A)=\dim\langle A\rangle-\dim A$ denote the defect of a subvariety $A$, where…

Let $Y\subset {\rm Sh}_K^0({\mathbf P},X)$ be a closed irreducible algebraic subvariety of a connected mixed Shimura variety. Classical André–Oort conjecture. If $Y$ contains a Zar…

Let $S$ be a connected mixed Shimura variety and let $Y$ be an irreducible subvariety of $S$. Mixed André–Oort conjecture. If the special points of $S$ contained in $Y$ are Zariski…

Let $S$ be a connected mixed Shimura variety associated with $(P,\mathcal{X}^+)$ and let $\mathrm{unif}\colon\mathcal{X}^+\to S$ be its uniformization. Let $\mathbscr{Z}$ be the gr…

Defect condition. Every mixed Shimura variety, and every weakly special subvariety, has the defect condition. The supplied span does not give the formal definition of the defect co…

Let $X$ be a mixed Shimura variety or a semi-abelian variety defined over $\mathbb{C}$. Let $\langle A\rangle$ denote the smallest special subvariety containing a subvariety $A$, a…

Let $\mathfrak{A}_g$ be the universal family of principally polarized abelian varieties, and let $Y$ be a subvariety of $\mathfrak{A}_g$. For $s\in\mathfrak{A}_g$, let $\Sigma$ be…

A mixed Shimura variety is an algebraic variety arising from a mixed Shimura datum; its special points and special subvarieties are the distinguished points and subvarieties define…

André–Oort–Pink conjecture. The set $\Sigma_{\mathrm{max}}(Z)$ is finite.