Lang-Weil type bounds in finite difference fields

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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.

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)