Versal torsors with a twist -- Zinovy Reichstein, March 28, 2014

The term “versal” is best understood by subtracting “unique” from both sides of the formula

Universal = unique + versal.

In this talk based on joint work with Alex Duncan, I will discuss competing notions of versality for the action of an algebraic group G on an algebraic variety X and relate these notions to properties (such as existence or density) of rational points on twisted forms of X. I will then present examples, where this relationship can be used to prove that certain group actons are versal or, conversely, that certain varieties have rational points.