Lazić–Peternell's generalized abundance conjecture

Let $X$ be a projective manifold with $K_X$ pseudoeffective, and let $L\to X$ be a nef line bundle such that

$$L^m\otimes K_X^{*}$$

is nef for some $m\geqslant 1$. Lazić–Peternell's generalized abundance conjecture. Then $L$ is numerically semiample. This is known only when the dimension is at most two, so the conjecture remains open in higher dimensions.