A dynamical approach to generalized Weil’s Riemann hypothesis

ALGEBRAIC DYNAMICS

Speaker:

Fei Hu - University of Oslo and Harvard University

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, I first discuss a special case of Abelian varieties. Then I will introduce the so-called dynamical correspondence and its application to certain surfaces. This is based on joint work with Tuyen Truong.

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