Journal article

### A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves

Abstract:
We state a conjectural criterion for identifying global integral points on a hyperbolic curve over $\Z$ in terms of Selmer schemes inside non-abelian cohomology functors with coefficients in $\Q_p$-unipotent fundamental groups. For $\P^1\setminus \{0,1,\infty\}$ and the complement of the origin in semi-stable elliptic curves of rank 0, we compute the local image of global Selmer schemes, which then allows us to numerically confirm our conjecture in a wide range of cases.
Publication status:
Submitted
Peer review status:
Under review
Version:
Author's Original

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More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Journal:
Annals of Mathematics
Publication date:
2014-01-01
URN:
uuid:a468799a-c621-42d2-bc10-fd9b357e1744
Source identifiers:
350706
Local pid:
pubs:350706
Keywords: