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Simplicity of the automorphism group of fields with operators

Thomas Blossier, Zoé Chatzidakis, Charlotte Hardouin and Amador Martin-Pizarro

Vol. 335 (2025), No. 2, 287–322
Abstract

We adapt a proof of Lascar in order to show the simplicity of the group of automorphisms fixing pointwise all nongeneric elements for a class of uncountable models of suitable theories, encompassing both strongly minimal theories as well as several theories of fields with operators.

Keywords
model theory, differentially closed fields, difference fields, automorphism groups
Mathematical Subject Classification
Primary: 03C45
Secondary: 12H05, 12H10
Milestones
Received: 26 November 2024
Revised: 31 March 2025
Accepted: 2 April 2025
Published: 30 April 2025
Authors
Thomas Blossier
Institut Camille Jordan UMR5208
Université Claude Bernard Lyon 1
Villeurbanne
France
Zoé Chatzidakis
IMJ-PRG
Université Paris Cité
Paris
France
Charlotte Hardouin
Institut de Mathématiques de Toulouse UMR5219
Université Paul Sabatier
Toulouse
France
Amador Martin-Pizarro
Abteilung für Mathematische Logik
Albert-Ludwigs-Universität Freiburg
Freiburg
Germany

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