Asok, Aravind; Hoyois, Marc; Wendt, Matthias Affine representability results in \(\mathbb A^1\)-homotopy theory. III: Finite fields and complements. (English) Zbl 07262981 Algebr. Geom. 7, No. 5, 634-644 (2020). Summary: We give a streamlined proof of \(\mathbb{A}^1\)-representability for G-torsors under “isotropic” reductive groups, extending previous results in this sequence of papers to finite fields. We then analyze a collection of group homomorphisms that yield fiber sequences in \(\mathbb{A}^1\)-homotopy theory, and identify the final examples of motivic spheres that arise as homogeneous spaces for reductive groups. MSC: 14F42 Motivic cohomology; motivic homotopy theory 14L10 Group varieties 55R15 Classification of fiber spaces or bundles in algebraic topology 20G15 Linear algebraic groups over arbitrary fields Keywords:torsors; algebraic groups; motivic homotopy theory PDF BibTeX XML Cite \textit{A. Asok} et al., Algebr. Geom. 7, No. 5, 634--644 (2020; Zbl 07262981) Full Text: DOI