9 problems

For $x otinboxminus$ a special point of the moduli space $mathcal{A}g$ of principally polarized abelian varieties, let $Ax$ be the corresponding $g$-dimensional principally polariz…

Let $\Gamma\subset G(\mathbb Q)$ be an arithmetic subgroup, let $S=\Gamma\backslash\Omega$, and let $V\subset\mathbb C^{N}\times S$ be an irreducible algebraic variety. Let…

Discriminant-negligibility conjecture. There exists a Weil height function $h\colon S(\overline{\mathbb Q})\to\mathbb R$ such that, for every special point $p\in S$ and every…

Effective André–Oort-type conjecture. There are effectively computable constants $c_i=c_i(V)$ such that whenever

Collinear triples conjecture. There are only finitely many triples with the $P_i$ pairwise distinct and lying on a straight line which is neither horizontal, vertical nor the diago…

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…

Soit $S$ une variété de Shimura et soit $\Sigma\subset S$ un ensemble de points spéciaux. Conjecture d'André–Oort. Les composantes irréductibles de l'adhérence de Zariski de…

Equidistribution conjecture. The sequence of measures $\Delta_{x_n}$ weakly converges to the canonical probability measure attached to…

Let $(G,X)$ be a Shimura $p$-datum, let $\operatorname{Sh}_{p}(G,X)$ be its integral model, and let $\mathbb{F}$ be the algebraic closure of the residue field. A point of…