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In this paper, we prove the abundance conjecture for threefolds over analgebraically closed field $k$ of characteristic $p > 3$ in the case ofnumerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ bea projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and$\nu(K_{X}+B)=2$, then $K_{X}+B$ is semiample.

Abundance for threefolds in positive characteristic when $\nu=2$