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We prove Iitaka's $C_{n,m}$ conjecture for $3$-folds over the algebraicclosure of finite fields. Along the way we prove some results on the birationalgeometry of log surfaces over nonclosed fields and apply these to existence ofrelative good minimal models of $3$-folds.

Iitaka's $C_{n,m}$ conjecture for 3-folds over finite fields