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arXiv · 1312.7019

Diophantine geometry and non-abelian reciprocity laws I

Minhyong Kim
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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.

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Minhyong Kim. 2013-12-25. Diophantine geometry and non-abelian reciprocity laws I. https://arxiv.org/abs/1312.7019

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