Non-invariance of weak approximation with Brauer--Manin obstruction

2022/03/18 by Wu, Han
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.09858

Abstract

In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension L/K, assuming a conjecture of M. Stoll, we prove that there exists a K-threefold satisfying weak approximation with Brauer--Manin obstruction off all archimedean places, while its base change to L fails. Then we illustrate this construction with an explicit unconditional example.

Related

• Non-invariance of weak approximation properties under extension of the ground field
• Non-invariance of the Brauer-Manin obstruction for surfaces
• The role of primes of good reduction in the Brauer--Manin obstruction
• Failures of weak approximation in families
• Châtelet surfaces and non-invariance of the Brauer-Manin obstruction for 3-folds