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We introduce a dynamical Mordell–Lang‐type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this conjecture for affinoid spaces, which we then use to prove our conjecture in the case of surfaces. These results rely on a module‐theoretic variant of Strassman's theorem that we prove in the appendix.

On a dynamical Mordell–Lang conjecture for coherent sheaves