Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 07 novembre 2019 à 11:30 - salle 430

Présentée par Javanpeykar Ariyan - Johannes Gutenberg Universität Mainz

Dynamics of varieties with only finitely many rational points

We present recent work with Junyi Xie in which we show that a variety over a number field with only finitely many rational points in any given number field has only finitely many dominant rational self-maps. This result is motivated by Lang-Vojta's conjecture. Indeed, such varieties should be of general type. We also prove similar results about varieties for which moduli spaces of maps from curves are bounded.