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
  M. 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). 
Silke Lekaus (Universit\"at Essen)