Principal bundles, quasi-abelian varieties and structure of algebraic groups

2008/06/23 by de Salas, Carlos Sancho, de Salas, Fernando Sancho
#14L15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0806.3712

Abstract

We classify principal bundles over anti-affine schemes with affine and commutative structural group. We show that this yields the classification of quasi-abelian varieties over a field k (i.e., group k-schemes with no non constant global functions). The interest of this result is given by the fact that the classification of smooth group k-schemes is reduced to the classification of quasi-abelian varieties and of certain affine group schemes.

Related

• Homogeneous bundles over abelian varieties
• Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics
• Some structure theorems for algebraic groups
• Pseudo-abelian varieties
• Principal bundles under reductive groups