On the fibration method for rational points

TL;DR

This paper investigates the fibration method to establish weak approximation for rationally connected varieties, exploring assumptions like strong approximation and Schinzel's hypothesis, and providing some unconditional results.

Contribution

It advances understanding of rational points on varieties by analyzing the fibration method under various hypotheses and presenting new unconditional results.

Findings

Weak approximation results under Schinzel's hypothesis

Conditional results assuming strong approximation for simple varieties

Some unconditional cases established

Abstract

We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.