Vojta's Main Conjecture

Let $X$ be a smooth projective variety defined over a number field $k$, let $K$ be a canonical divisor, let $A$ be an ample divisor, and let $D$ be a reduced normal-crossings divisor. Let $S$ be a finite subset of $M_k$.

Vojta's Main Conjecture. Given $\epsilon > 0$, there exists a Zariski-closed subset $Z=Z_\epsilon eq X$ such that

$$\sum_{v\in S} \lambda_v(D,P)+h(K,P)\leq \epsilon h(A,P)$$

for all $P\in (X\setminus Z)(k)$.

This is Vojta's predicted height inequality for rational points outside a proper exceptional subset. The supplied context identifies it as Vojta's Main Conjecture; no resolution status is given here.