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Vector Bundles on an Elliptic Curve

Published online by Cambridge University Press:  22 January 2016

Tadao Oda
Tadao Oda*
Affiliation:
Mathematical Institute, Nagoya University
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971 , pp. 41 - 72
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

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