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

Voir la notice de l'article provenant de la source EMS Press

DOI

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
@article{10_4171_emss_47,
     author = {Ehud Hrushovski},
     title = {Ax{\textquoteright}s theorem with an additive character},
     journal = {EMS surveys in mathematical sciences},
     pages = {179--216},
     year = {2021},
     volume = {8},
     doi = {10.4171/emss/47},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/47/}
}
TY  - JOUR
AU  - Ehud Hrushovski
TI  - Ax’s theorem with an additive character
JO  - EMS surveys in mathematical sciences
PY  - 2021
SP  - 179
EP  - 216
VL  - 8
UR  - http://geodesic.mathdoc.fr/articles/10.4171/emss/47/
DO  - 10.4171/emss/47
ID  - 10_4171_emss_47
ER  - 
%0 Journal Article
%A Ehud Hrushovski
%T Ax’s theorem with an additive character
%J EMS surveys in mathematical sciences
%D 2021
%P 179-216
%V 8
%U http://geodesic.mathdoc.fr/articles/10.4171/emss/47/
%R 10.4171/emss/47
%F 10_4171_emss_47

Cité par Sources :