Diophantine geometry and non-abelian reciprocity laws I
Number Theory
2015-05-18 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1312.7019,
title = {Diophantine geometry and non-abelian reciprocity laws I},
author = {Minhyong Kim},
journal= {arXiv preprint arXiv:1312.7019},
year = {2015}
}
Comments
Corrected some errors, including replacing fundamental group by prime-to-2 quotient