• Abelianization of the $F$-divided fundamental group scheme

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/127/02/0281-0287

• # Keywords

$F$-divided fundamental group scheme; Frobenius; Picard scheme; Albanese

• # Abstract

Let ($X , x_0$) be a pointed smooth proper variety defined over an algebraically closed field. The Albanese morphism for ($X , x_0$) 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.

• # Author Affiliations

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
2. Institut de Mathematiques de Jussieu – Paris Rive Gauche, 4 Place Jussieu, Case 247, 75252 Paris Cedex 5, France

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019