Arithmetic purity of strong approximation for complete toric varieties

TL;DR

This paper proves that strong approximation with Brauer-Manin obstruction holds for smooth loci of weighted projective spaces and extends this result to all smooth, complete toric varieties using descent methods.

Contribution

It establishes the arithmetic purity of strong approximation for weighted projective spaces and generalizes it to all smooth, complete toric varieties.

Findings

Strong approximation with Brauer-Manin obstruction holds for smooth loci of weighted projective spaces.

The result extends to all smooth, complete toric varieties.

Uses descent method to generalize the purity result.

Abstract

In this article, we establish the arithmetic purity of strong approximation for smooth loci of weighted projective spaces. By using this result and the descent method, we also prove that the arithmetic purity of strong approximation with Brauer-Manin obstruction holds for any smooth and complete toric variety.