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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.

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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}
}

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Revised version. All comments are welcome