𝔸¹-connectedness in reductive algebraic groups

Balwe, Chetan; Sawant, Anand

doi:10.1090/tran/7090

$\mathbb {A}^1$-connectedness in reductive algebraic groups
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by Chetan Balwe and Anand Sawant PDF

Trans. Amer. Math. Soc. 369 (2017), 5999-6015 Request permission

Corrigendum: Trans. Amer. Math. Soc. 369 (2017), 8317-8317.

Abstract:

Using sheaves of $\mathbb {A}^1$-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be $\mathbb {A}^1$-local if the group does not satisfy suitable isotropy hypotheses. As a consequence, we show the failure of $\mathbb {A}^1$-invariance of torsors for such groups on smooth affine schemes over infinite perfect fields. We also characterize $\mathbb {A}^1$-connected reductive algebraic groups over a field of characteristic $0$.

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