On the dynamical Mordell-Lang conjecture in positive characteristic

We prove that the dynamical Mordell-Lang conjecture in positive characteristic holds for bounded-degree self-maps of projective varieties. The key ingredient of the proof is a Mordell-Lang-type result for arbitrary algebraic groups over algebraically closed fields of positive characteristic, which is also interesting on its own. Moreover, we propose a geometric version of dynamical Mordell-Lang conjecture in positive characteristic.