A dynamical approach to Weil’s Riemann hypothesis - Fei Hu

Speaker: Fei Hu
Affiliation: University of Oslo
Date: June 23, 2021

Abstract: Inspired by a result of Esnault and Srinivas on automorphisms of surfaces and recent advances in complex dynamics, Truong raised a question on the comparison of two dynamical degrees, which are defined using pullback actions of dynamical correspondences on numerical cycle class groups and cohomology groups, respectively. An affirmative answer to his question would surprisingly imply Weil’s Riemann hypothesis. In this talk, we consider more comparison problems on the norms and spectral radii of the pullback actions of certain correspondences. I will talk about their connections with Truong’s dynamical degree comparison and the standard conjectures. Under certain technical assumption, some partial results will be given. I will also discuss some applications to Abelian varieties and surfaces. This is based on joint work with Tuyen Truong.