On cubic torsors, biextensions and Severi-Brauer varieties over Abelian varieties

Abstract

We study the homogeneous irreducible Severi-Brauer varieties over an Abelian variety $A$. Such objects were classified by Brion, \cite{Bri}. Here we interpret that result within the context of cubical structures and biextensions for certain $\G_m$-torsors over finite subgroups of $A$. Our results can be seen as an instance of the theory developed by Breen, \cite{Breen:1983}, and Moret-Bailly, \cite{Moret-Bailly}.

Final Version. Several Improvements. Published by Sao Paulo J. Math. Sci

References in corpus (3)

• Self cup products and the theta characteristic torsor
• Homogeneous projective bundles over abelian varieties
• Homogeneous vector bundles over abelian varieties via representation theory