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A DIOPHANTINE DEFINITION OF THE CONSTANTS IN Q(z)
| Indexado |
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| DOI | 10.1090/PROC/17034 | ||||
| Año | 2025 | ||||
| Tipo | artículo de investigación |
Citas Totales
Autores Afiliación Chile
Instituciones Chile
% Participación
Internacional
Autores
Afiliación Extranjera
Instituciones
Extranjeras
Abstract
It is an old problem in the area of Diophantine definability to determine whether Q is Diophantine in Q (z). Conditional on two standard conjectures on elliptic surfaces, we provide a positive answer; namely, we show that such a Diophantine definition exists.
| Ord. | Autor | Género | Institución - País |
|---|---|---|---|
| 1 | Garcia-fritz, Natalia | - |
Pontificia Universidad Católica de Chile - Chile
Facultad de Matemáticas - Chile |
| 2 | Pasten, Hector | - |
Pontificia Universidad Católica de Chile - Chile
Facultad de Matemáticas - Chile |
| Agradecimiento |
|---|
| We thank Thanases Pheidas for encouraging us to work on this problem and we thank Jerson Caro for his feedback on a first version of this manuscript. We are grateful to Arno Fehm for answering several questions. We also thank the anonymous referees for their valuable suggestions.This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while the authors participated in the program Definability, Decidability, and Computability in Number Theory, part 2, hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Summer of 2022. |
| We thank Thanases Pheidas for encouraging us to work on this problem and we thank Jerson Caro for his feedback on a first version of this manuscript. We are grateful to Arno Fehm for answering several questions. We also thank the anonymous referees for their valuable suggestions. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while the authors participated in the program Definability, Decidability, and Computability in Number Theory, part 2, hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Summer of 2022 |
