Some remarks on the affineness of A^1-bundles

Abstract: We study how forcing algebras give rise to ${\mathbb A}^1$-bundles and ${\mathbb A}^1$-torsors and how they are related to ${\mathbb A}^1$-patches. In particular we discuss the affineness of torsors and how algebraic properties of ${\mathbb A}^1$-patches can be deduced from this property. This is in part a survey article.