4 problems

Let $\Gamma\backslash X^+$ be a Shimura variety, let $V$ be an algebraic subvariety of it, and let $x\in X^+$. Write ${\mathcal{H}}_{\Gamma\backslash X^+}(x)$ for the generalised H…

Let $\Gamma\backslash X^+$ be an arithmetic variety, let $V$ be an irreducible algebraic subvariety, let $(M,X_M)$ be a Shimura datum, and let $x\in X_M$ be Hodge generic. Write…

Let $S$ be a Shimura variety and let $obreakboldsymbol{Xi} obreakto S$ be a subset of the generalised Hecke orbit of a point in $S$. Write $obreakboldsymbol{bar{Xi}} obreak$ for…

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…