Twisted Lang-Weil estimates and definable quotients

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Abstract

By a celebrated result of Ax from the 60s, everything non-trivial that can be said about ’large’ finite fields follows from the Lang-Weil estimates. This may be made precise with the help of so-called pseudofinite fields. A twisted version of the Lang-Weil estimates, due to Hrushovski, leads to an analogous result on the q-Frobenius automorphism, where q is a ’large’ prime power, ultimately showing that the non-standard Frobenius automorphism satisfies a Nullstellensatz for difference polynomials. In the talk, we will first give an overview of these results, and we will then present a classification of definable quotients in algebraically closed fields endowed with a non-standard Frobenius automorphism, also in case a non-trivial valuation is added to the structure.

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)