Abelianization of the F-divided fundamental group scheme

2016/01/19 by Indranil Biswas, Biswas, Indranil, João Pedro P. dos Santos +1
Mathematics · #14F35 #14G17 #14K30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1601.04955

openalex publication_date 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X ,x₀) be a pointed smooth proper variety defined over an algebraically closed field. The Albanese morphism for (X ,x₀) produces a homomorphism from the abelianization of the F-divided fundamental group scheme of X to the F-divided fundamental group of the Albanese variety of X. We prove that this homomorphism is surjective with finite kernel. The kernel is also described.

Related

• Albanese maps and fundamental groups of varieties with many rational points over function fields
• Albanese maps for open algebraic spaces
• Fundamental group-scheme of some rationally connected fibrations
• The Albanese morphism for hyperelliptic varieties
• Para-abelian varieties and Albanese maps