Some aspects of rational points and rational curves

Abstract

Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context (rational points over number fields) and in an algebro-geometric one (rational curves on real varieties), and discuss the question of rational points over function fields of p-adic curves.

arXiv comment20 pages; for the ICM 2022 proceedings; v2: updated bibliography, final version