Abundance in numerical dimension one for terminal threefolds in positive characteristic

Abstract — v1

Let $X$ be a projective $\mathbb Q$-factorial terminal threefold over an algebraically closed field of characteristic $p\gt 3$. We prove the numerical-dimension-one case of abundance: if $K_X$ is nef with $\nu(K_X)=1$, then $K_X$ is semiample and $\kappa(X,K_X)=1$.