Fundamental groups and Diophantine geometry

2008/04/07 by Kim, Minhyong
#14G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0804.1008

Abstract

We give a brief exposition on the uses of non-commutative fundamental groups for the study of Diophantine problems via a non-abelian Albanese map.

Related

• Galois theory and Diophantine geometry
• Remark on fundamental groups and effective Diophantine methods for hyperbolic curves
• Diophantine geometry and non-abelian reciprocity laws I
• From uncountable abelian groups to uncountable nonabelian groups
• Albanese maps and fundamental groups of varieties with many rational points over function fields