Geodesic
Ax’s theorem with an additive character
Ehud Hrushovski1 orcid
1University of Oxford, UK
EMS surveys in mathematical sciences, Tome 8 (2021), pp. 179-216

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Motivated by Emmanuel Kowalski’s exponential sums over definable sets in finite fields, we generalize Ax’s theorem on pseudo-finite fields to a continuous-logic setting allowing for an additive character. The role played byWeil’s Riemann hypothesis for curves over finite fields is taken by the ‘Weil bound’ on exponential sums. Subsequent model-theoretic developments, including simplicity and the Chatzidakis–Van den Dries–Macintyre definable measures, also generalize.
DOI : 10.4171/emss/47
Classification : 03-XX, 11-XX
Mots-clés : Decidability, finite fields, additive character

Ehud Hrushovski  1

1 University of Oxford, UK 
Ehud Hrushovski. Ax’s theorem with an additive character. EMS surveys in mathematical sciences, Tome 8 (2021), pp. 179-216. doi: 10.4171/emss/47
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     title = {Ax{\textquoteright}s theorem with an additive character},
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     year = {2021},
     volume = {8},
     doi = {10.4171/emss/47},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/47/}
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