Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

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.