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Affine representability results in ${\mathbb A}^{1}$-homotopy theory III: Finite fields and complements

Asok, Aravind ; Hoyois, Marc ; Wendt, Matthias


We give a streamlined proof of 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 A(1)-homotopy theory, and identify the final examples of motivic spheres that arise as homogeneous spaces for reductive groups.

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