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The elliptic sieve and Brauer groups
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Bhakta, Subham, Loughran, Daniel, Rydin Myerson, Simon L. and Nakahara, Masahiro (2023) The elliptic sieve and Brauer groups. Proceedings of the London Mathematical Society, 126 (6). pp. 1884-1922. doi:10.1112/plms.12520 ISSN 0024-6115 .
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Proceedings of London Math Soc - 2023 - Bhakta - The elliptic sieve and Brauer groups.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (350Kb) | Preview |
Official URL: https://doi.org/10.1112/plms.12520
Abstract
A theorem of Serre states that almost all plane conics over Q ${{\mathbb {Q}}}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves. We also give more general results for specialisations of Brauer groups, which yields applications to norm form equations.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
SWORD Depositor: | Library Publications Router | ||||||||||||
Library of Congress Subject Headings (LCSH): | Number theory, Curves, Algebraic, Sieves (Mathematics), Arithmetical algebraic geometry, Brauer groups | ||||||||||||
Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||||||||||
Publisher: | Cambridge University Press | ||||||||||||
ISSN: | 0024-6115 | ||||||||||||
Official Date: | June 2023 | ||||||||||||
Dates: |
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Volume: | 126 | ||||||||||||
Number: | 6 | ||||||||||||
Page Range: | pp. 1884-1922 | ||||||||||||
DOI: | 10.1112/plms.12520 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Copyright Holders: | © 2023 The Authors. Proceedings of the London Mathematical Society is copyright © London Mathematical Society. | ||||||||||||
Date of first compliant deposit: | 16 May 2023 | ||||||||||||
Date of first compliant Open Access: | 17 May 2023 | ||||||||||||
RIOXX Funder/Project Grant: |
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