6 problems

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…

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…