4 problems

Let $\mathcal{M}$ be a smooth quasi-projective complex variety with universal covering $\mathcal{M}^u$. Let $\mathbb{D}$ be a Hermitian symmetric domain of noncompact type, and let…

Hodge–Zucker conjecture. The isomorphism in Theorem 2.8 is an isomorphism of $\mathbb{R}$-Hodge structures. The question refines Zucker's conjecture by asking whether its cohomolog…

Let $p$ be a prime, $D$ a Hermitian symmetric domain, $G=\operatorname{Aut}^0(D)$, and let $\Gamma$ be an arithmetic subgroup of $G$ as in the source. For a subgroup…

Let $K$ be the field corresponding to a ball arising from a symmetric cubic fourfold. Field conjecture. For all balls arising from symmetric cubic fourfolds, the corresponding fiel…