Group Theory Seminar
Profinite Rigidity over Noetherian Domains
Speaker: Julian Wykowski (Cambridge)Date: Thursday, 24 April 2025 - 11:00Place: Aula Naranja, ICMAT
Abstract:
Profinite rigidity of groups asks whether the isomorphism type of a group can be determined entirely in the collection of its finite quotients. In this talk, I will introduce the study of profinite rigidity in a different category, namely the category of modules over a Noetherian domain Λ. I will present some foundational results and explore which properties of Λ-modules are profinitely invariant. I will explain how these properties may be used to obtain profinite rigidity results for free Λ-modules under a homological assumption on Λ and for all modules in the case where Λ is a Dedekind domain or PID. Finally, I will sketch some applications of this theory for the profinite rigidity of certain classes of solvable groups.
