Model Theory Seminar | Rahim Moosa | Around the wild automorphism conjecture

Rahim Moosa (University of Waterloo)

Around the wild automorphism conjecture

The wild automorphism conjecture, of Reichstein, Rogalski, and Zhang from 2006, proposes that if a projective algebraic variety X (in characteristic zero) admits an automorphism that leaves no proper subvariety invariant then X is an abelian variety. I will discuss recent work with Jason Bell where we use tools from the model theory of difference fields (developed last year by Moshe Kamensky and I) to resolve the “compound fundamental isotrivial” case. I will also give a counterexample to the naive nonautonomous generalisation of the conjecture, exhibiting some of the difficulties in applying a model-theoretic analysis.

MC 5403