Vector Bundles on an Elliptic Curve

1 September 1971

journal article
research article
Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal

Vol. 43, 41-72
https://doi.org/10.1017/s0027763000014367

Abstract

Let k be an algebraically closed field of characteristic p≧ 0, and let X be an abelian variety over k.The goal of this paper is to answer the following questions, when dim(X) = 1 and p≠0, posed by R. Hartshorne: (1)Is E(P) indecomposable, when E is an indecomposable vector bundle on X? (2)Is the Frobenius map F^*: H¹ (X, E) → H¹ (X, E^(p)) injective?We also partly answer the following question posed by D. Mumford: (3)Classify, or at least say anything about, vector bundles on X when dim (X) > 1.

Keywords

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