# On rationally connected varieties over $C_1$ fields of characteristic $0$

## TL;DR

This paper demonstrates that rational points on proper rationally connected varieties over characteristic zero fields follow from rational points on terminal Fano varieties, advancing the understanding of the $C_1$-conjecture.

## Contribution

It establishes a link between rational points on rationally connected varieties and terminal Fano varieties over $C_1$ fields of characteristic zero, providing new insights into the $C_1$-conjecture.

## Key findings

- Rational points on rationally connected varieties depend on those on terminal Fano varieties.
- Evidence supporting the $C_1$-conjecture in dimension 3 for characteristic zero fields.
- Implications for the $C_1$-conjecture based on birational geometry techniques.

## Abstract

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic $0$ is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequences of this result, especially in relation to the $C_1$-conjecture. We also provide evidence that supports the conjecture in dimension $3$ for $C_1$ fields of characteristic $0$.