Non-invariance of weak approximation with Brauer--Manin obstruction
Abstract
In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension assuming a conjecture of M. Stoll, we prove that there exists a -threefold satisfying weak approximation with Brauer--Manin obstruction off all archimedean places, while its base change to fails. Then we illustrate this construction with an explicit unconditional example.
Keywords
Cite
@article{arxiv.2203.09858,
title = {Non-invariance of weak approximation with Brauer--Manin obstruction},
author = {Han Wu},
journal= {arXiv preprint arXiv:2203.09858},
year = {2022}
}
Comments
This is a part of our paper "Ch\^atelet surfaces and non-invariance of the Brauer--Manin obstruction for 3-folds" arXiv:2010.04919. The part on "the Hasse principle with Brauer-Manin obstruction" is being considered by the editor of manuscripta mathematica. So we reorganize the rest part, and simplify the construction of Ch\^atelet surfaces to make it more readable