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

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

2008-06-23

arxiv.org/abs/0806.3712v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

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.

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