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 $(X,\Delta)$ such that $K_X +\Delta\equiv M \geq 0$ over bases of positive and mixed characteristic $p>5$.