Strong approximation and a conjecture of Harpaz and Wittenberg

TL;DR

This paper investigates strong approximation properties for certain algebraic varieties defined by norm forms over the rationals, confirming a specific case of a conjecture by Harpaz and Wittenberg.

Contribution

It provides a proof of a special case of the Harpaz-Wittenberg conjecture related to strong approximation on norm form varieties.

Findings

Confirmed a case of the Harpaz-Wittenberg conjecture

Established strong approximation for norm form varieties over rationals

Enhanced understanding of rational points on algebraic varieties

Abstract

We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.