Affine representability results in 1–homotopy theory, II : Principal bundles and homogeneous spaces

By A. Asok, Marc Hoyois, Matthias Wendt. 2015

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We establish a relative version of the abstract "affine representability" theorem in ${\mathbb A}^1$--homotopy theory from Part I of this paper. We then prove some ${\mathbb A}^1$--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 ${\mathbb A}^1$--homotopy theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3cdd587088ff615695241aad6b57bf918ee76144