R-equivalence on group schemes
Algebraic Geometry
2025-11-17 v4 Rings and Algebras
Abstract
We define R-equivalence for group schemes over a semilocal ring and relate this with rational properties. Two main cases are investigated: tori and isotropic semisimple simply connected group schemes where we show in certain cases that R-equivalence coincide with Karoubi-Villamayor equivalence and is also related to the Kneser-Tits problem in this setting. Finally we construct specialization maps for R-equivalence in the case of regular algebras containing a field.
Cite
@article{arxiv.2107.01950,
title = {R-equivalence on group schemes},
author = {Philippe Gille and A Stavrova},
journal= {arXiv preprint arXiv:2107.01950},
year = {2025}
}