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

Abstract: In this talk we will discuss topological properties of varieties with many rational points over a function field, and present joint work-in-progress with Erwan Rousseau. More precisely, we define a smooth projective variety X over the complex numbers to be geometrically-special if there is a dense set of closed points S in X such that, for every x in S, there is a pointed curve (C,c) and a sequence of morphisms (C,c)->(X,x) which covers C x X, i.e., the union of their graphs is Zariski-dense in C x X. Roughly speaking, a variety is geometrically-special if it satisfies density of "pointed" rational points over some function field. Inspired by conjectures of Campana on special varieties and Lang on hyperbolic varieties, we prove that every linear quotient of the fundamental group pi_1(X) of such a variety is virtually abelian.

algebraic geometry

Audience: researchers in the topic

Western Algebraic Geometry ONline

Series comments: Description: Conference in algebraic geometry

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