Tame Structures via Multiplicative Character Sums on Varieties over Finite Fields
نویسنده
چکیده
We study the model theory of (F;<χ) where the field F is an algebraic closure of a finite field and <χ is an ordering on the multiplicative group F× induced by a group embedding χ ∶ F× → C×. Using number-theoretic bounds on multiplicative character sums over finite fields and Weyl’s criterion for equidistribution, we establish a number of properties about the interaction between <χ and the underlying field structure. We obtain a first-order axiomatization of these properties and show that the resulting theory is strongly model complete and has NTP2.
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تاریخ انتشار 2017