Affine representability results in A^1-homotopy theory II: principal bundles and homogeneous spaces

Abstract

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.

45 pages; To appear Geom & Top.; final version before page proofs

References in corpus (1)

• Affine representability results in ${\mathbb{A}}^1$-homotopy theory I: vector bundles

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