Algebraic Groups with Torsors That Are Versal for All Affine Varieties

Uriya A. First, Mathieu Florence, Zev Rosengarten

Let $k$ be a field and let $G$ be an affine algebraic group over $k$. Call a $G$-torsor weakly versal for a class of $k$-schemes $\mathcal{C}$ if it specializes to every $G$-torsor over…