Weak approximation on Ch\^{a}telet surfaces
Number Theory
2022-06-22 v1 Algebraic Geometry
Abstract
We study weak approximation for Ch\^{a}telet surfaces over number fields when all singular fibers are defined over rational points. We consider Ch\^{a}telet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer-Manin obstruction vanishes, then apply results of Colliot-Th\'el\`ene, Sansuc, and Swinnerton-Dyer.
Keywords
Cite
@article{arxiv.2206.10556,
title = {Weak approximation on Ch\^{a}telet surfaces},
author = {Masahiro Nakahara and Samuel Roven},
journal= {arXiv preprint arXiv:2206.10556},
year = {2022}
}
Comments
14 pages