Albanese maps and fundamental groups of varieties with many rational points over function fields

2020/10/06 by Javanpeykar, Ariyan, Rousseau, Erwan · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.02913

Abstract

We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is virtually abelian, as well as that its Albanese map is surjective, has connected fibres, and has no multiple fibres in codimension one.

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• Hyperbolicity and fundamental groups of complex quasi-projective varieties (III): applications
• More counterexamples to the Arithmetic Puncturing Problem

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