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2018 Affine representability results in $\mathbb{A}^1$–homotopy theory, II: Principal bundles and homogeneous spaces
Aravind Asok, Marc Hoyois, Matthias Wendt
Geom. Topol. 22(2): 1181-1225 (2018). DOI: 10.2140/gt.2018.22.1181

Abstract

We establish a relative version of the abstract “affine representability” theorem in A1–homotopy theory from part I of this paper. We then prove some A1–invariance statements for generically trivial torsors under isotropic reductive groups over infinite fields analogous to the Bass–Quillen conjecture for vector bundles. Putting these ingredients together, we deduce representability theorems for generically trivial torsors under isotropic reductive groups and for associated homogeneous spaces in A1–homotopy theory.

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Aravind Asok. Marc Hoyois. Matthias Wendt. "Affine representability results in $\mathbb{A}^1$–homotopy theory, II: Principal bundles and homogeneous spaces." Geom. Topol. 22 (2) 1181 - 1225, 2018. https://doi.org/10.2140/gt.2018.22.1181

Information

Received: 13 July 2016; Revised: 25 April 2017; Accepted: 24 May 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 06828607
MathSciNet: MR3748687
Digital Object Identifier: 10.2140/gt.2018.22.1181

Subjects:
Primary: 14F42, 14L10, 20G15, 55R15

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.22 • No. 2 • 2018
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