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On asymptotic Fermat over the Z_2 extension of Q
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Freitas, Nuno, Kraus, Alain and Siksek, Samir (2021) On asymptotic Fermat over the Z_2 extension of Q. Annales Mathématiques Blaise Pascal, 28 (1). pp. 1-6. doi:10.5802/ambp.397 ISSN 2118-7436.
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Official URL: https://doi.org/10.5802/ambp.397
Abstract
In a recent work the authors prove the effective asymptotic Fermat’s Last Theorem for the infinite family of fields where . A crucial step in their proof is the following conjecture of Kraus. Let be a number field having odd narrow class number and a unique prime above . Then there are no elliptic curves defined over with conductor and a -rational point of order . In this note we give a new elementary proof of Kraus’ conjecture that makes use only of basic facts about elliptic curves, Tate curves and Tate modules
| 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): | Curves, Elliptic, Fermat's last theorem, Algebraic fields | |||||||||
| Journal or Publication Title: | Annales Mathématiques Blaise Pascal | |||||||||
| Publisher: | Le laboratoire de mathématiques Blaise Pascal | |||||||||
| ISSN: | 2118-7436 | |||||||||
| Official Date: | 21 January 2021 | |||||||||
| Dates: |
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| Volume: | 28 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 1-6 | |||||||||
| DOI: | 10.5802/ambp.397 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 7 July 2020 | |||||||||
| Date of first compliant Open Access: | 10 July 2020 | |||||||||
| RIOXX Funder/Project Grant: |
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