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

Carlos Sancho de Salas; Fernando Sancho de Salas

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arXiv · 0806.3712

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

Carlos Sancho de Salas·Fernando Sancho de Salas

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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.

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Carlos Sancho de Salas, Fernando Sancho de Salas. 2008-06-23. Principal bundles, quasi-abelian varieties and structure of algebraic groups. https://arxiv.org/abs/0806.3712

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