A Simpler Approach to a Descent Conjecture of Wittenberg
Algebraic Geometry
2026-04-14 v2 Number Theory
Abstract
A descent conjecture of Wittenberg [Wit24, Conjecture 3.7.4] predicts that if all the twists of a rationally connected torsor over a smooth base satisfy weak approximation with Brauer-Manin obstruction, then so does the base. We give an alternative proof of Wittenberg's conjecture for certain torsors under connected linear groups via Cao's descent formula.
Keywords
Cite
@article{arxiv.2604.08146,
title = {A Simpler Approach to a Descent Conjecture of Wittenberg},
author = {Yisheng Tian},
journal= {arXiv preprint arXiv:2604.08146},
year = {2026}
}
Comments
Revised version. All comments are welcome