Diophantine geometry and non-abelian reciprocity laws I

Abstract

We use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The non-abelian reciprocity law then states that the global points are contained in the kernel of all the reciprocity maps.Comment: Corrected some errors, including replacing fundamental group by prime-to-2 quotien