Classification of imaginaries in valued fields with automorphism.

Basic data for this talk

Type of talk: scientific Talk

Name der Vortragenden: Hils, Martin

Date of talk: 25/02/2020

Talk language: English

Information about the event

Name of the event: Logic Seminar

Event period: 25/02/2020

Event location: The Hebrew University of Jerusalem, Jerusalem, Israel

Abstract

The imaginaries in the theory ACVF of non-triviallally valued algebraically closed valued fields are classified by the so-called 'geometric' sorts. This is a fundamental result due to Haskell-Hrushovski-Macpherson. We show that the imaginaries in henselian equicharacteristic 0 valued fields may be reduced, under rather general assumptions, to the geometric sorts and to imaginaries in RV together with sorts for certain finite-dimensional vector spaces over the residue field. In the talk, I will mainly speak about an application of this reduction, which has been the initial motivation of our work: The imaginaries in the theory VFA of algebraically closed non-trivially valued fields of equicharacteristic 0, endowed with a non-standard Frobenius automorphism, are classified by the geometric sorts. This requires an understanding of imaginaries in pure short exact sequences, and a key result from Hrushovski's groupoids paper.

Keywords: model theory; classification of imaginaries; valued fields with automorphism

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)

Projects the talk is about

Geometric and Combinatorial Configurations in Model Theory (GeoMod) Duration: 01/01/2020 - 31/12/2024 Funded by: DFG - Individual Grants Programme Type of project: Individual project
Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure (EXC 2044) Duration: 01/01/2019 - 31/12/2025 \| 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Main DFG-project hosted at University of Münster
SFB 878 A09 - Geoöetric Moel Theory of Valued Fields Duration: 01/09/2016 - 30/06/2019 \| 1st Funding period Funded by: DFG - Collaborative Research Centre Type of project: Subproject in DFG-joint project hosted at University of Münster

Publications referred to in the talk

Un principe d'Ax-Kochen-Ershov imaginaire

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