Geometry & Topology

Affine representability results in $\mathbb{A}^1$–homotopy theory, II: Principal bundles and homogeneous spaces

Aravind Asok, Marc Hoyois, and Matthias Wendt

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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.

Article information

Source
Geom. Topol., Volume 22, Number 2 (2018), 1181-1225.

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1517454118

Digital Object Identifier
doi:10.2140/gt.2018.22.1181

Mathematical Reviews number (MathSciNet)
MR3748687

Zentralblatt MATH identifier
06828607

Subjects
Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15] 14L10: Group varieties 20G15: Linear algebraic groups over arbitrary fields 55R15: Classification

Keywords
motivic homotopy theory principal bundles

Citation

Asok, Aravind; Hoyois, Marc; Wendt, Matthias. Affine representability results in $\mathbb{A}^1$–homotopy theory, II: Principal bundles and homogeneous spaces. Geom. Topol. 22 (2018), no. 2, 1181--1225. doi:10.2140/gt.2018.22.1181. https://projecteuclid.org/euclid.gt/1517454118


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