Rational points and zero-cycles on rationally connected varieties over number fields

TL;DR

This paper reviews recent progress in understanding rational points, zero-cycles, and integral points on rationally connected varieties over number fields, emphasizing connections with analytic number theory.

Contribution

It synthesizes recent developments and highlights the interplay between algebraic geometry and analytic number theory in the study of rational points.

Findings

Advances in the qualitative understanding of rational points.

New insights into zero-cycles and integral points.

Enhanced connections between algebraic geometry and analytic number theory.

Abstract

We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties. One of the main objectives is to highlight and explain the many recent interactions with analytic number theory.