Time：14:00, Friday, May 10 2024
Venue：E4-233
Speaker：Yugang Zhang, Université Paris-Saclay
Title：Finiteness results for families of plane regular polynomial automorphisms
Abstract：Given a marked point of an algebraic family of rational maps on the projective line, there are infinitely many preperiodic points by Montel's theorem. As a special case, there are infinitely many torsion points on a section of a family of elliptic curves. Now given a family of simple abelian varieties of relative dimension larger than 1, the subset of torsion points are not Zariski dense in any non-torsion section, by a recent result of Gao and Habegger. We propose a dynamical analogue of this result for families of Hénon maps defined over number fields.
