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Balwe, Chetan and Sawant, Anand (2017): A(1)-connectedness in reductive algebraic GROUPS1. In: Transactions of the American Mathematical Society, Vol. 369, No. 8: pp. 5999-6015

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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 a field of characteristic 0.

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