Profinite Rigidity, Noetherian Domains, and Solvable Groups

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• Julian Wykowski (University of Cambridge)
• Tuesday 29 July 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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OGGW01 - Discrete and profinite groups

The profinite rigidity of a discrete group Γ is intimately related to the profinite rigidity of Γ-module representations. The quest for understanding the profinite rigidity of groups thus calls for a systematic theory of profinite rigidity in algebraic categories. In this talk, I will present a framework for the study of profinite rigidity in the category of modules over a Noetherian domain Λ. I will explore profinite invariants for Λ-modules over any Noetherian domain Λ, as well as absolute profinite rigidity results in the presence of certain homological assumptions on Λ. I will then go on to discuss applications to the profinite rigidity of solvable groups. In particular, I will sketch a proof that solvable Baumslag–Solitar groups and free metabelian groups are profinitely rigid in the absolute sense. These are the first known examples of absolute profinite rigidity among non-abelian one-relator groups and among non-LERF groups.

This talk is part of the Isaac Newton Institute Seminar Series series.

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