Classification of imaginaries in existentially closed valued difference fields
Basic data for this talk
Type of talk: scientific Talk
Name der Vortragenden: Hils, Martin
Date of talk: 04/03/2022
Talk language: English
Information about the event
Name of the event: Research Seminar
Event period: 04/03/2022
Event location: Università degli Studi di Napoli Federico II
Abstract
In their seminal work, Haskell, Hrushovski and Macpherson gave a classification of imaginaries (i.e. quotient objects in the definable category) in an algebraically closed valued field K by the so-called geometric sorts, namely the valued field sort together with sorts for all OK-lattices in Kn and for the reducts of these lattices modulo the maximal ideal of the valuation ring OK. In the talk, I will present recent work, joint with Silvain Rideau-Kikuchi, establishing that the geometric sorts are also sufficient to classify the imaginaries in certain existentially closed valued difference fields of residue characteristic 0, in particular in the isometric case, where the automorphism induces the identity on the value group, and in the omega-increasing case, which corresponds to the non-standard Frobenius automorphism acting on an algebraically closed valued field.Keywords: model theory; valued fields; difference fields; classification of imaginaries
Speakers from the University of Münster
| Hils, Martin |
Projects the talk is about
Duration: 01/01/2020 - 31/12/2024 Funded by: DFG - Individual Grants Programme Type of project: Individual project | |
Duration: 01/01/2019 - 31/12/2025 | 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Subproject in DFG-joint project hosted at University of Münster |
Publications referred to in the talk
Hils Martin, Rideau-Kikuchi Silvain (2026) In: Journal of the European Mathematical Society, 28(3), 1009-1080. doi:10.4171/JEMS/1492 Research article (journal) | Peer reviewed | Published |