Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields

Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields

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 surject...

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Veröffentlicht in:International mathematics research notices 2022-12, Vol.2022 (24), p.19354-19398
Hauptverfasser: Javanpeykar, Ariyan, Rousseau, Erwan
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Rousseau, Erwan
description 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.
doi_str_mv 10.1093/imrn/rnab255
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source Oxford University Press Journals All Titles (1996-Current)
title Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields
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