Biswas, Indranil ; Hein, Georg
(2009)
*Generalization of a criterion for semistable vector bundles*
Finite Fields and Their Applications, 15
(5).
pp. 580-584.
ISSN 1071-5797

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S10715...

Related URL: http://dx.doi.org/10.1016/j.ffa.2009.06.001

## Abstract

It is known that a vector bundle E on a smooth projective curve Y defined over an algebraically closed field is semistable if and only if there is a vector bundle F on Y such that both H^{0}(X,E⊗ F) and H^{1}(X,E⊗F) vanishes. We extend this criterion for semistability to vector bundles on curves defined over perfect fields. Let X be a geometrically irreducible smooth projective curve defined over a perfect field k, and let E be a vector bundle on X. We prove that E is semistable if and only if there is a vector bundle F on X such that H^{i}(X,E⊗F)=0 for all i. We also give an explicit bound for the rank of F.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Moduli Space; Vector Bundles on a Curve; Generalized Theta Divisor |

ID Code: | 3549 |

Deposited On: | 12 Oct 2010 04:16 |

Last Modified: | 12 Oct 2010 04:16 |

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