Non-archimedean Lang–Vojta conjecture

Let $K$ be an algebraically closed complete non-archimedean valued field of characteristic zero. A variety $X$ over $K$ is $K$-analytically Brody hyperbolic if every morphism from the analytification $G^{\operatorname{an}}$ of a finite-type connected group scheme $G$ over $K$ to $X^{\operatorname{an}}$ is constant. Non-archimedean Lang–Vojta conjecture. If $X$ is a projective groupless variety over $K$, then $X$ is $K$-analytically Brody hyperbolic. This conjecture proposes the converse to the implication that $K$-analytically Brody hyperbolicity implies grouplessness; the source provides no resolution status.