Abstract: Fix a finite group G. We seek to classify varieties with G-action equivariantly birational to a representation of G on affine or projective space. The equivariant rationality problem is analogous to Diophantine questions over nonclosed fields. We explore how invariants – both classical cohomological invariants and recent symbol constructions – control rationality in some cases. Universal torsors are a powerful geometric tool for analyzing equivariant stable birational equivalence. (joint with Tschinkel)
Ref: B. Hassett and Y. Tschinkel, Torsors and stable equivariant birational geometry
