Arithmetic of Ch\^atelet surface bundles revisited
Algebraic Geometry
2021-12-07 v2 Number Theory
Abstract
We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming the finiteness of the Tate-Shafarevich group of a certain elliptic curve, we show, for Ch\^atelet surface bundles over curves, that the violation of Hasse principle being accounted for by the Brauer-Manin obstruction is not invariant under an arbitrary finite extension of the ground field.
Keywords
Cite
@article{arxiv.2106.10643,
title = {Arithmetic of Ch\^atelet surface bundles revisited},
author = {Guang Hu and Yongqi Liang},
journal= {arXiv preprint arXiv:2106.10643},
year = {2021}
}
Comments
Comments are welcome