Versal Varieties with a Twist
Alexander Duncan, UCLA
Let G be a linear algebraic group. Informally, a versal G-torsor is a G-torsor
(over a field) from which one can recover any other G-torsor. Versal torsors
behave similarly to universal objects, but fail to satisfy certain uniqueness
properties. In this talk, I introduce several variations of the notion of
versality for a G-variety X. These notions have equivalent formulations as
properties of twisted forms of X: existence of k-points, density of k-points,
k-unirationality and so on.
This is joint work with Zinovy Reichstein.