Vector bundles on the moduli stack of elliptic curves

Abstract

We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles. For R=Z(3), we construct higher rank indecomposable vector bundles and give a classification of vector bundles that are iterated extensions of line bundles. If R=Z(2), we show that there are even indecomposable vector bundles of arbitrary high rank.