A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves
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 s...
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| Format: | Journal article |
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2014
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| _version_ | 1826289015304749056 |
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| author | Balakrishnan, J Dan-Cohen, I Kim, M Wewers, S |
| author_facet | Balakrishnan, J Dan-Cohen, I Kim, M Wewers, S |
| author_sort | Balakrishnan, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:22:27Z |
| format | Journal article |
| id | oxford-uuid:a468799a-c621-42d2-bc10-fd9b357e1744 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:22:27Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:a468799a-c621-42d2-bc10-fd9b357e17442022-03-27T02:33:42ZA non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a468799a-c621-42d2-bc10-fd9b357e1744Symplectic Elements at Oxford2014Balakrishnan, JDan-Cohen, IKim, MWewers, SWe 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. |
| spellingShingle | Balakrishnan, J Dan-Cohen, I Kim, M Wewers, S A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves |
| title | A non-abelian conjecture of Birch and Swinnerton-Dyer type for
hyperbolic curves |
| title_full | A non-abelian conjecture of Birch and Swinnerton-Dyer type for
hyperbolic curves |
| title_fullStr | A non-abelian conjecture of Birch and Swinnerton-Dyer type for
hyperbolic curves |
| title_full_unstemmed | A non-abelian conjecture of Birch and Swinnerton-Dyer type for
hyperbolic curves |
| title_short | A non-abelian conjecture of Birch and Swinnerton-Dyer type for
hyperbolic curves |
| title_sort | non abelian conjecture of birch and swinnerton dyer type for hyperbolic curves |
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