$\mathbb {A}^1$-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 $0$.References
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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
- MR Author ID: 677361
- Email: cbalwe@iisermohali.ac.in
- Anand Sawant
- Affiliation: Mathematisches Institut, Ludwig-Maximilians Universität, Theresienstr. 39, D-80333 München, Germany
- Email: sawant@math.lmu.de
- Received by editor(s): May 17, 2016
- Received by editor(s) in revised form: October 3, 2016
- Published electronically: March 31, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 5999-6015
- MSC (2010): Primary 14F42, 14L15, 55R10
- DOI: https://doi.org/10.1090/tran/7090
- MathSciNet review: 3646787