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: 26/01/2023

Talk language: English

Information about the event

Name of the event: Logic Colloquium

Event period: 26/01/2023

Event location: Universität Wien

Event website: https://mathematik.univie.ac.at/forschung/seminare/seminars-at-the-kgrc/nachrichtenvolldarstellung-se/news/lang-weil-type-bounds-in-finite-difference-fields/?no_cache=1&cHash=dc40252068dd4c561144b20f2d641e98

Organised by: Kurt Gödel Research Center, Universität Wien

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 the transformal dimension of p, i.e., to the maximal transformal transcendence degree over K of a realization of p. This is joint work with Ehud Hrushovski, Jinhe Ye and Tingxiang Zou.

Keywords: Lang-Weil estimates; finite difference fields; non-standard counting

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
EXC 2044 - A2: Groups, model theory and sets 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