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arXiv · 1408.6627

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

Chetan Balwe·Anand Sawant
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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.

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Chetan Balwe, Anand Sawant. 2014-08-28. R-equivalence and A^1-connectedness in anisotropic groups. https://arxiv.org/abs/1408.6627

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