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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

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Official URL: https://doi.org/10.1073/pnas.2026449118

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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
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:
DateEvent
23 March 2021Published
17 February 2021Accepted
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
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/S031537/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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