Contre-exemples au principe de Hasse pour certains tores coflasques

TL;DR

This paper investigates the failure of the Hasse principle in certain algebraic varieties using an explicit Brauer-Manin obstruction description, revealing insights into their density and distribution.

Contribution

It provides a detailed analysis of the Brauer-Manin obstruction for specific varieties, advancing understanding of when the Hasse principle fails.

Findings

Identifies conditions under which varieties violate the Hasse principle.

Quantifies the density of such varieties within a family.

Utilizes explicit Brauer-Manin obstruction descriptions for analysis.

Abstract

We use an explicit description of the Brauer-Manin obstruction, recently obtained by Colliot-Th\'el\`ene, to study the density of varieties in a certain family which do not satisfy the Hasse principle.