Journal article icon

Journal article

An effective Chabauty-Kim theorem

Abstract:
The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

Actions


Access Document


Files:
Publisher copy:
10.1112/S0010437X19007243

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Jesus College
Role:
Author
Publisher:
Foundation Compositio Mathematica Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
155
Issue:
6
Pages:
1057-1075
Publication date:
2019-05-14
Acceptance date:
2019-01-24
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
Pubs id:
pubs:983813
URN:
uri:197c48e8-486b-4680-87ac-8dd1b4ddf108
UUID:
uuid:197c48e8-486b-4680-87ac-8dd1b4ddf108
Local pid:
pubs:983813

Terms of use


Metrics


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP