Lang-Weil type bounds in finite difference fields
Basic data for this talk
Type of talk: scientific Talk
Name der Vortragenden: Hils, Martin
Date of talk: 15/02/2023
Talk language: English
Information about the event
Name of the event: Donau-Rhein-Modelltheorie-Seminar
Event period: 14/02/2023 - 15/02/2023
Event location: Universität Passau
Event website: https://www.fim.uni-passau.de/professur-reine-mathematik/donau-rhein-modelltheorie-seminar
Abstract
We establish Lang-Weil type bounds for the number of rational points of difference varieties over finite difference fields, in terms of the transformal dimension of the variety and assuming the existence of a smooth rational point. It follows that, working in any non-principle ultraproduct K of finite difference fields, the normalized pseudofinite dimension of a quantifier free partial type p is equal to its transformal dimension, i.e., to the maximal transformal transcendence degree over K of a realization of p. The proof uses a strong form of the Lang-Weil estimates (due to Cafure and Matera) and, as key ingredient to obtain equidimensional Frobenius specializations, the recent work of Dor and Hrushovski on the non-standard Frobenius acting on an algebraically closed non-trivially valued field, in particular the pure stable embeddedness of the residue difference field in this context. This is joint work with Ehud Hrushovski, Jinhe Ye and Tingxiang Zou.Keywords: Lang-Weil estimates; finite difference field; non-standard counting
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 |