On a Dynamical Mordell-Lang Conjecture for Coherent Sheaves

TL;DR

This paper formulates a dynamical Mordell-Lang conjecture for coherent sheaves, proves an analogue for affinoid spaces, and confirms the conjecture for surfaces using a module-theoretic variant of Strassman's theorem.

Contribution

It introduces a new conjecture linking dynamics and coherent sheaves, proves an analogue in affinoid spaces, and verifies the conjecture for surfaces.

Findings

Proved the conjecture for surfaces.

Established an analogue for affinoid spaces.

Developed a module-theoretic version of Strassman's theorem.

Abstract

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.