5 problems

Let \overline{X} = \overline{{\left.\raisebox{-.2em}{Gamma}\middle\backslash\raisebox{.2em}{mathbb B^n}\right.}} be a compactification as in Theorem, with $n \geq 6$. Here…

Let $(X, \Delta)$ be a smooth C-pair over $\mathbb{C}$, where a dense entire curve means a holomorphic C-pair map $\mathbb{C} \to (X, \Delta)^{\an}$ whose image is Zariski-dense in…

Let $X$ be a smooth quasi-projective variety. A variety is pseudo-Picard hyperbolic if it satisfies the punctured-disk extension property outside a proper Zariski closed subset, an…

Relative Green-Griffiths-Lang conjecture. The following conditions are equivalent:

Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let $X/K$ be a projective variety. Say that $X$ is groupless over $K$ when it…