Back to Algebraic Geometry Seminar: Spring 2016
Algebraic Geometry Seminar
Date: Tuesday, Feb 23, 2016
Time: 3:30PM - 4:30PM
Location: JFB 102
2:50 - 3:50PM LCB 219
John Lesieutre
University of Illinois at Chicago
Title |
Dynamical Mordell--Lang and automorphisms of higher-dimensional varieties |
Abstract |
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 to study dynamically interesting (e.g. positive entropy) automorphisms of complex varieties in higher dimensions. This is joint work with Daniel Litt. |
Algebraic Geometry