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

Nathan Grieve

doi:10.1007/s40863-021-00250-3

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

Algebraic Geometry 2021-08-11 v2

Authors: Nathan Grieve

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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}.

Keywords

severi-brauer varieties abelian varieties cubic torsors biextensions cubical structures gm-torsors

Cite

@article{arxiv.1807.01663,
  title  = {On cubic torsors, biextensions and Severi-Brauer varieties over Abelian varieties},
  author = {Nathan Grieve},
  journal= {arXiv preprint arXiv:1807.01663},
  year   = {2021}
}

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

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

Abstract

Keywords

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