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A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves

Abstract:

Let X denote a hyperbolic curve over Q and let p denote a prime of good reduction. The third author’s approach to integral points, introduced in Kim (Invent Math 161:629–656, 2005; Publ Res Inst Math Sci 45:89–133, 2009), endows X(Zp) with a nested sequence of subsets X(Zp)n which contain X(Z). These sets have been computed in a range of special cases (Balakrishnan et al., J Am Math Soc 24:281–291, 2011; Dan-Cohen and Wewers, Proc Lond Math Soc 110:133–171, 2015; Dan-Cohen and Wewers, Int Mat...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1007/s00208-018-1684-x

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Mathematische Annalen Journal website
Volume:
372
Issue:
1-2
Pages:
369–428
Publication date:
2018-06-30
Acceptance date:
2017-05-01
DOI:
EISSN:
1432-1807
ISSN:
0025-5831
Pubs id:
pubs:695460
URN:
uri:2bf0593a-46e2-41f7-adda-278611203eae
UUID:
uuid:2bf0593a-46e2-41f7-adda-278611203eae
Local pid:
pubs:695460

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