John Lesieutre - Dynamical Mordell--Lang and automorphisms of higher-dimensional varieties

May 10, 2016 - Princeton University
This talk was part of the Princeton-Tokyo Algebraic Geometry Conference

The dynamical Mordell--Lang conjecture predicts that if $f$ is an endomorphism of a complex variety $X$, with $p$ a point of $X$ and $V$ a subvariety, then the set of $n$ for which $f^n(p)$ lands in $V$ is a union of a finite set and finitely many arithmetic progressions. When $f$ is \'etale, this is a result of Bell--Ghioca--Tucker. I'll discuss an extension of this result to the setting in which $p$ and $V$ are non-reduced closed subschemes of $X$, and show how this statement can be applied geometrically to obtain constraints on automorphisms of higher-dimensional varieties. This is joint work with Daniel Litt.