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Local criteria for the unit equation and the asymptotic Fermat's Last Theorem
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Freitas, Nuno, Kraus, Alain and Siksek, Samir (2021) Local criteria for the unit equation and the asymptotic Fermat's Last Theorem. Proceedings of the National Academy of Sciences of the United States of America, 118 (12). e2026449118. doi:10.1073/pnas.2026449118 ISSN 0027-8424.
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Official URL: https://doi.org/10.1073/pnas.2026449118
Abstract
Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat’s Last Theorem to hold over F and also, for the nonexistence of solutions to the unit equation over F. For example, if two totally ramifies and three splits completely in F, then the asymptotic Fermat’s Last Theorem holds over F.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Fermat's last theorem , Galois theory | ||||||
| Journal or Publication Title: | Proceedings of the National Academy of Sciences of the United States of America | ||||||
| Publisher: | National Academy of Sciences | ||||||
| ISSN: | 0027-8424 | ||||||
| Official Date: | 23 March 2021 | ||||||
| Dates: |
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| Volume: | 118 | ||||||
| Number: | 12 | ||||||
| Article Number: | e2026449118 | ||||||
| DOI: | 10.1073/pnas.2026449118 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 17 February 2021 | ||||||
| Date of first compliant Open Access: | 23 September 2021 | ||||||
| RIOXX Funder/Project Grant: |
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