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

Abstract

We study homogeneous irreducible Severi–Brauer varieties over an Abelian variety A. Such objects were classified by Brion (Algebra Number Theory 7(10):2475–2510, 2013). Here we interpret that result within the context of cubic structures and biextensions for certain \(\mathbb {G}_m\)-torsors over finite subgroups of A. Our results build on the theory of Breen (Fonctions thêta et théorème du cube, Springer, Berlin, 1983), and Moret-Bailly (Pinceaux de variétés abéliennes. Astérisque 129:266, 1985).