Relation between the dimensions of the ring generated by a vector bundle of degree zero on an elliptic curve and a torsor trivializing this bundle

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59511M. Nori proved that on a projective smooth variety, a bundle is finite, (that is the ring it generates has dimension 0), if and only if it trivializes on a finite cover. In this note, we consider bundles of degree 0 on an elliptic curve. We prove that the dimension of the ring generated by such a bundle is the same as the dimension of a torsor trivializing the bundle (and is 1).Latex2e, 7 pagesAlgebraic GeometryRelation between the dimensions of the ring generated by a vector bundle of degree zero on an elliptic curve and a torsor trivializing this bundletext