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: 11/01/2023
Talk language: English
Information about the event
Name of the event: Model Theory: Combinatorics, Groups, Valued Fields and Neostability
Event period: 08/01/2023 - 14/01/2023
Event location: Mathematisches Forschungsinstitut Oberwolfach
Event website: https://publications.mfo.de/handle/mfo/4040
Abstract
(joint work with Ehud Hrushovski, Jinhe Ye and Tingxiang Zou) We prove 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 in (certain) non-principle ultraproducts of finite difference fields the course dimension of a quantifier free type equals its transformal transcendence degree. The proof uses a strong form of the Lang-Weil estimates 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.Keywords: Lang-Weil type bounds; 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 |