Generalization of a criterion for semistable vector bundles

Details Generalization of a criterion for semistable vector bundles Generalization of a criterion for semistable vector bundles

2008-04-25

arxiv.org/abs/0804.4120v1

Mathematics

Algebraic Geometry

Scientific paper

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 the cohomologies of E\otimes F vanish. 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 the cohomologies of E\otimes F vanish. We also give an explicit bound for the rank of $F$.

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