English

R-equivalence and A^1-connectedness in anisotropic groups

Algebraic Geometry 2016-10-07 v1

Abstract

We show that if G is an anisotropic, semisimple, absolutely almost simple, simply connected group over a field k, then two elements of G over any field extension of k are R-equivalent if and only if they are A^1-equivalent. As a consequence, we see that Sing_*(G) cannot be A^1-local for such groups. This implies that the A^1-connected components of a semisimple, absolutely almost simple, simply connected group over a field k form a sheaf of abelian groups.

Keywords

Cite

@article{arxiv.1408.6627,
  title  = {R-equivalence and A^1-connectedness in anisotropic groups},
  author = {Chetan Balwe and Anand Sawant},
  journal= {arXiv preprint arXiv:1408.6627},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-22T05:42:26.570Z