Non-invariance of weak approximation with Brauer-Manin obstruction for surfaces
Number Theory
2022-09-05 v1 Algebraic Geometry
Abstract
In this paper, we study the property of weak approximation with Brauer-Manin obstruction for surfaces with respect to field extensions of number fields. For any nontrivial extension of number fields L/K, assuming a conjecture of M. Stoll, we construct a smooth, projective, and geometrically connected surface over K such that it satisfies 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.
Keywords
Cite
@article{arxiv.2209.00893,
title = {Non-invariance of weak approximation with Brauer-Manin obstruction for surfaces},
author = {Han Wu},
journal= {arXiv preprint arXiv:2209.00893},
year = {2022}
}
Comments
This is a part of our paper "Non-invariance of the Brauer-Manin obstruction for surfaces" arXiv:2103.01784