%0 Journal Article
%T A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves
%A Jennifer Balakrishnan
%A Ishai Dan-Cohen
%A Minhyong Kim
%A Stefan Wewers
%J Mathematics
%D 2012
%I arXiv
%X We state a conjectural criterion for identifying global integral points on a hyperbolic curve over $\mathbb{Z}$ in terms of Selmer schemes inside non-abelian cohomology functors with coefficients in $\mathbb{Q}_p$-unipotent fundamental groups. For $\mathbb{P}^1\setminus \{0,1,\infty\}$ 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.
%U http://arxiv.org/abs/1209.0640v3