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Ax's theorem with an additive character

Abstract:

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 by Weil’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.

Analytically,...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/EMSS/47

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0002-2761-6513
Publisher:
EMS Press Publisher's website
Journal:
EMS Surveys in Mathematical Sciences Journal website
Volume:
8
Issue:
1-2
Pages:
179-216
Publication date:
2021-08-31
Acceptance date:
2021-08-31
DOI:
EISSN:
2308-216X
ISSN:
2308-2151
Language:
English
Keywords:
Pubs id:
1197898
Local pid:
pubs:1197898
Deposit date:
2022-03-01

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