Affine representability results in A^1-homotopy theory III: finite fields and complements
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.03365
- arXiv:
- arXiv:1807.03365
- Bibcode:
- 2018arXiv180703365A
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Algebraic Topology;
- Mathematics - Group Theory;
- Mathematics - K-Theory and Homology;
- 14F42;
- 14L10;
- 55R15;
- 20G15
- E-Print:
- 9 pages