A^1-connectedness in reductive algebraic groups

Chetan Balwe, Anand Sawant

Published 2016-05-15Version 1

Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be A^1-local if the group does not satisfy suitable isotropy hypotheses. As a consequence, we show the failure of A^1-invariance of torsors for such groups on smooth affine schemes over infinite perfect fields. We also characterize A^1-connected reductive algebraic groups over an infinite perfect field and use this characterization to study relationship of A^1-connectedness with R-equivalence.