Tame structures via character sums over finite fields

Chieu-Minh Tran

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arXiv · 1704.03853

Tame structures via character sums over finite fields

Chieu-Minh Tran

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Abstract

We show that the theory of algebraically closed fields with multiplicative circular orders has a model companion $\mathrm{ACFO}$. Using number-theoretic results on character sums over finite fields, we show that if $\mathbb{F}$ is an algebraic closure of a finite field, and $\triangleleft$ is any translation-invariant circular order on the multiplicative group $\mathbb{F}^\times$, then $(\mathbb{F}, \triangleleft)$ is a model of $\mathrm{ACFO}$. Our results can be regarded as analogues of Ax's results in [1] which utilize counting points over finite fields.

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BibTeX RIS

Chieu-Minh Tran. 2017-04-12. Tame structures via character sums over finite fields. https://arxiv.org/abs/1704.03853

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