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

Ariyan Javanpeykar (1) , Erwan Rousseau (2, 3)

1 Fachbereich Mathematik der Johannes-Gutenberg
2 IUF - Institut universitaire de France
3 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Ariyan Javanpeykar, Erwan Rousseau. Albanese maps and fundamental groups of varieties with many rational points over function fields. 2020. ⟨hal-02959690⟩