13 problems

Let $A$ be an abelian variety over $K=\mathbb C(S)$, where $S/\mathbb C$ is a curve, and let $F$ be the field of meromorphic functions on a disc in $S$. Let…

Let $G/\mathbb{Q}_p$ be a reductive group, let $[\mu]$ be a minuscule conjugacy class of cocharacters of $G_{\overline{\mathbb{Q}}_p}$, and let $b\in G(\breve{\mathbb{Q}}_p)$ repre…

Let $\textnormal{S}_{\alpha}$ be a stratum of abelian differentials up to scaling, let $\widetilde{\textnormal{S}_{\alpha}^{\mathrm{an}}}$ be the universal cover of its analytifica…

Let $q: Omegato S$ be the quotient map associated with the Shimura setting, and let $EqsubsetOmegatimes S$ denote its graph. Let $Vsubsetmathbb C^{N}times S$ be an irreducible alge…

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 $C$ be an algebraically closed field with $\operatorname{td}(C/\mathbb{Q})=\aleph_0$, let $\mathfrak{C}$ be the class of $E_j$-fields with constant field $C$, and let $U$ be it…

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…

Let $S^\natural$ be a connected enlarged mixed Shimura variety associated with $(P,\mathcal{X}^{\natural+})$, with uniformization…

Let $\pi:\mathbb{H}\rightarrow S$ be the uniformizing maps of a Shimura variety $S$ corresponding to a semisimple group $G$. Let $k\geq 2$ and let…

Let $\pi:\mathbb{H}_g\rightarrow \mathcal{A}_g$ be the classical uniformisation of the moduli space of principally polarised abelian varieties of dimension $g$. Let $\Gamma$ be the…

Let $A$ be as in the complex Modular Ax-Schanuel setting, with geodesically independent coordinates $z_1,\ldots,z_n$ and the modular function $j$. Modular Ax-Schanuel conjecture wi…

Let $X=Y(1)^n$ with uniformising map $\pi:\mathbb{H}^n\to X(\mathbb{C})$. For a subvariety $V\subseteq X$, a component is an irreducible component of $W\cap\pi^{-1}(V)$ for an alge…

Let $U$ be a domain in $\mathbb{H}^n$, let $U'$ be a geodesic subvariety of $U$, and put $X'=\exp U'$. Let $A$ be a complex-analytic component of $W\cap\pi^{-1}(V)$, where…