Algebraic actions II. Groupoid rigidity
Abstract
Abstract We establish several surprising rigidity results for étale groupoids associated with algebraic actions. Our initial motivation comes from algebraic number theory, where our results are witnessed in a particularly striking fashion. We prove that the groupoids associated with the action of the multiplicative monoid in a ring of algebraic integers on the additive group of the ring remember the ring up to isomorphism. Already, this special case resolves an open problem about isomorphisms of Cartan pairs and leads to a dynamical analogue of the Neukirch–Uchida theorem using topological full groups.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Geometric and Algebraic Topology
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 5
- Pages
- 1213–1246
- Publication date
- 1 May 2026
- Language
- EN