The modular approach to Diophantine equations over totally real fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909063378370560 |
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| author | Khawaja, Maleeha Siksek, Samir |
| author_facet | Khawaja, Maleeha Siksek, Samir |
| contents | Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $\mathbb{Q}$. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine equations over totally real number fields. We give an extensive overview of these obstacles as well as providing a survey of existing methods and results in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The modular approach to Diophantine equations over totally real fields Khawaja, Maleeha Siksek, Samir Number Theory 11D41, 11F80, 11F41 Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $\mathbb{Q}$. Numerous novel obstacles arise when extending this approach to the resolution of Diophantine equations over totally real number fields. We give an extensive overview of these obstacles as well as providing a survey of existing methods and results in this area. |
| title | The modular approach to Diophantine equations over totally real fields |
| topic | Number Theory 11D41, 11F80, 11F41 |
| url | https://arxiv.org/abs/2401.03099 |