Lang-Weil Type Estimates in Finite Difference Fields
Number Theory
2024-06-04 v1 Algebraic Geometry
Logic
Abstract
We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a difference variety in terms of its transformal dimension. As a main technical ingredient, we prove an equidimensionality result for Frobenius reductions of difference varieties.
Keywords
Cite
@article{arxiv.2406.00880,
title = {Lang-Weil Type Estimates in Finite Difference Fields},
author = {Martin Hils and Ehud Hrushovski and Jinhe Ye and Tingxiang Zou},
journal= {arXiv preprint arXiv:2406.00880},
year = {2024}
}