弱逼近关于 Brauer--Manin 阻碍的非不变性
数论
2022-03-21 v1
摘要
本文研究关于数域扩张的带 Brauer--Manin 阻碍的弱逼近。对任意非平凡扩张 ，在假设 M. Stoll 的一个猜想下，我们证明存在一个 -三维簇满足去掉所有阿基米德位的带 Brauer--Manin 阻碍的弱逼近，而其基变换到 后不成立。随后我们用一个显式无条件例子说明该构造。
引用
@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}
}
备注
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