Weak approximation of symmetric products and norm varieties

TL;DR

This paper investigates the weak approximation property with Brauer-Manin obstruction for symmetric products and norm varieties over number fields, extending known results to these classes of varieties.

Contribution

It introduces methods to analyze weak approximation with Brauer-Manin obstruction for symmetric products and norm varieties, expanding the understanding of rational points on these varieties.

Findings

Weak approximation extends to symmetric products under certain conditions.

Weak approximation with Brauer-Manin obstruction applies to norm varieties.

Methodology unifies approach for symmetric products and norm varieties.

Abstract

Let k be a number field. For a variety X over k that satisfies weak approximation with Brauer-Manin obstruction, we study the same property for smooth projective models of its symmetric products. Based on the same method, we also explore the property of weak approximation with Brauer-Manin obstruction for norm varieties.