The behavior of essential dimension under deformations

Abstract: Let k be a field of characteristic zero, G be a linear algebraic k-group, and n a non-negative integer. We show that in a flat family of primitive generically free G-varieties over a base k-variety B, the points of B whose geometric fiber has essential dimension at most n form a countable union of closed subsets of B. As an application, we construct unramified non-versal G-torsors of maximal essential dimension. This is joint work with Zinovy Reichstein.

algebraic geometrygroup theorynumber theoryrepresentation theory

Audience: researchers in the topic

Algebraic groups and algebraic geometry: in honor of Zinovy Reichstein's 60th birthday