Expansive endomorphisms of profinite groups

Abstract: Étale algebraic groups over a field k are equivalent to finite groups with a continuous action of the absolute Galois group of k. The difference version of this well-know result asserts that étale difference algebraic groups over a difference field k (i.e., a field equipped with an endomorphism) are equivalent to profinite groups equipped with an expansive endomorphism and a certain compatible difference Galois action. In any case, understanding the structure of expansive endomorphisms of profinite groups seems a worthwhile endeavor and that's what this talk is about.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle