Diophantine geometry and non-abelian reciprocity laws I

2013/12/25 by Kim, Minhyong
#11D99 #11R37 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1312.7019

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.

Related

• Galois theory and Diophantine geometry
• Lectures on the cohomology of reciprocity sheaves
• Fesenko reciprocity map
• Fundamental groups and Diophantine geometry
• Simplicial Abel-Jacobi maps and reciprocity laws