Lyubeznik's étale cohomological dimension conjecture

Let $U$ be a scheme of finite type over a separably closed field $\mathbb{K}$. Write $\operatorname{\acute{e}cd}(U)$ for its étale cohomological dimension and $\operatorname{qccd}(U)$ for its quasicoherent cohomological dimension.

Lyubeznik's conjecture.

$$\operatorname{\acute{e}cd}(U) \geq \dim(U)+\operatorname{qccd}(U).$$

The conjecture compares étale and quasicoherent cohomological dimensions. It was motivated by examples in which the étale-cohomological lower bound is at least as strong as the quasicoherent one; its resolution is not specified here.