Exponentially closed fields and the conjecture on intersections with tori |
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Authors: | Jonathan Kirby Boris Zilber |
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Affiliation: | 1. School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom;2. Mathematical Institute, University of Oxford, 24–29 St Giles'', Oxford OX1 3LB, United Kingdom |
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Abstract: | We give an axiomatization of the class ECF of exponentially closed fields, which includes the pseudo-exponential fields previously introduced by the second author, and show that it is superstable over its interpretation of arithmetic. Furthermore, ECF is exactly the elementary class of the pseudo-exponential fields if and only if the Diophantine conjecture CIT on atypical intersections of tori with subvarieties is true. |
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Keywords: | 03C65 03C35 03C60 11U09 |
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