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Quadratic Chabauty and rational points II: generalised height functions on Selmer varieties

Abstract:
We give new instances where Chabauty–Kim sets can be proved to be finite, by developing a notion of “generalised height functions” on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals and give the 1st explicit nonabelian Chabauty result for a curve X/Q whose Jacobian has Mordell–Weil rank larger than its genus.
Publication status:
Published
Peer review status:
Peer reviewed

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Files:
  • (Accepted manuscript, pdf, 609.1KB)
Publisher copy:
10.1093/imrn/rnz362

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Jesus College
Role:
Author
ORCID:
0000-0003-3475-5383
Publisher:
Oxford University Press
Journal:
International Mathematics Research Notices More from this journal
Volume:
2021
Issue:
15
Pages:
11923-12008
Publication date:
2020-02-01
Acceptance date:
2019-12-04
DOI:
EISSN:
1687-0247
ISSN:
1073-7928
Language:
English
Keywords:
Pubs id:
pubs:1076479
UUID:
uuid:9133a425-796f-4e05-8a09-7b05eacf9559
Local pid:
pubs:1076479
Source identifiers:
1076479
Deposit date:
2019-12-05

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