9 problems

The Lang–Vojta conjecture. Under these hypotheses, every set of $(D,S)$-integral points in $X$ is Zariski degenerate. These problems are central in Diophantine geometry and, for th…

Consequence of the extended Lang–Vojta conjecture. There is a proper closed subset $\Delta\subsetneq U$ such that:

Extended Lang–Vojta conjecture. The following conditions are equivalent:

Lang–Vojta conjecture. The stated degree inequality holds uniformly for all such curves and morphisms outside the proper exceptional subset $Z$.

Let $k$ be an algebraically closed field of characteristic zero and let $X$ be a projective variety over $k$. Let $\Delta_X^{\mathrm{gr}}$, $\Delta_X^{\mathrm{Mor}}$,…

Let $k$ be an algebraically closed field of characteristic zero. For a projective variety $X$ over $k$, consider strong pseudo-Brody and pseudo-Kobayashi hyperbolicity, pseudo-Mord…

Let $k$ be an algebraically closed field of characteristic zero. A variety over $k$ is strongly-pseudo-Brody hyperbolic (respectively, strongly-pseudo-Kobayashi hyperbolic) if ever…

Let $k$ be an algebraically closed field of characteristic zero. For a projective variety $X$ over $k$, consider pseudo-Mordellicity, pseudo-arithmetic hyperbolicity, pseudo-groupl…

Let $k$ be an algebraically closed field of characteristic zero. A variety $X$ over $k$ is strongly-Brody hyperbolic over $k$ if, for every subfield $k_0\subset k$, every model…