Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Alex Carney, UC Berkeley
Inviter:
Title:
The arithmetic Hodge-index theorem and dynamical systems
Time & Venue:
2018.10.19 14:30-15:30 N818
Abstract:
The hodge-index theorem in classical algebraic geometry states that the signature of the intersection form on a surface is +1,-1,...,-1. In one of the fundamental results of Arakelov theory, Faltings and Hriljac extend this to arithmetic surfaces by relating the intersection pairing to the negative of the Neron-Tate height pairing. In this talk, I'll explain how Yuan and Zhang (in the number field case) and my work (in the function field case) generalize this to higher dimensional varieties. An important use of arithmetic intersection theory is in defining height functions of both points and subvarieties, and as an example I will show how the hodge index theorem is used to prove a rigidity theorem for preperiodic points in algebraic dynamical systems.