English

Generically isotropic reductive group schemes are locally isotropic

Algebraic Geometry 2023-04-12 v2

Abstract

Let RR be a semilocal geometrically factorial Noetherian domain of characteristic zero. We show that a reductive RR-group scheme is isotropic if it is generically isotropic. We derive various consequences, in particular for the Grothenieck-Serre conjecture and for homotopic invariance of torsors.

Keywords

Cite

@article{arxiv.2303.05853,
  title  = {Generically isotropic reductive group schemes are locally isotropic},
  author = {Roman Fedorov},
  journal= {arXiv preprint arXiv:2303.05853},
  year   = {2023}
}

Comments

Existence part of Proposition 3.13 is incorrect invalidating the argument. I am looking for a remedy

R2 v1 2026-06-28T09:10:55.133Z