Lang–Vojta + Chevalley–Weil implication

Prove that if a variety X over a number field has a potentially dense set of integral points, then X is weakly special.

Background

Lang and Vojta conjectured non-density of integral points on varieties of log-general type. Combining this with the Chevalley–Weil theorem suggests a one-way implication from potential density to weak specialness.

The paper formulates this implication explicitly as a conjecture connecting arithmetic potential density to the geometric property of being weakly special.

References

Conjecture [Lang--Vojta + Chevalley--Weil]\label{conj:lv} Let $X$ be a variety over a number field. If $X$ satisfies potential density of integral points, then $X$ is weakly special.

— Weakly special varieties, Campana stacks, and Remarks on Orbifold Mordell  (2603.28745 - Bartsch et al., 30 Mar 2026) in Introduction, Special varieties (Conjecture \ref{conj:lv})