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$ \mathbb{A}^1$-connectedness in reductive algebraic groups


Authors: Chetan Balwe and Anand Sawant
Journal: Trans. Amer. Math. Soc. 369 (2017), 5999-6015
MSC (2010): Primary 14F42, 14L15, 55R10
DOI: https://doi.org/10.1090/tran/7090
Published electronically: March 31, 2017
Corrigendum: Trans. Amer. Math. Soc. 369 (2017), 8317-8317.
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Chetan Balwe
Affiliation: Department of Mathematics, Indian Institute of Science Education and Research (IISER), Knowledge City, Sector-81, Mohali 140306, India
Email: cbalwe@iisermohali.ac.in

Anand Sawant
Affiliation: Mathematisches Institut, Ludwig-Maximilians Universität, Theresienstr. 39, D-80333 München, Germany
Email: sawant@math.lmu.de

DOI: https://doi.org/10.1090/tran/7090
Received by editor(s): May 17, 2016
Received by editor(s) in revised form: October 3, 2016
Published electronically: March 31, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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