The cone theorem for effective fourfold pairs in characteristic $p>5$

Abstract: Assuming the log resolution conjecture for all log pairs birational to $X$, we prove the cone theorem for projective log canonical, $\mathbb{Q}$-factorial fourfold pairs $(X,Δ)$ such that $K_X +Δ\equiv M \geq 0$ over bases of positive and mixed characteristic $p > 5$.