Generalization of a criterion for semistable vector bundles

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dc.creatorBiswas, Indranil
dc.creatorHein, Georg
dc.date2008-04-25
dc.date.accessioned2026-07-07T09:35:19Z
dc.date.available2026-07-07T09:35:19Z
dc.descriptionIt 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 $F$.
dc.identifierhttps://arxiv.org/abs/0804.4120
dc.identifierhttp://arxiv.org/abs/0804.4120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159796
dc.subjectAlgebraic Geometry
dc.subject14F05
dc.titleGeneralization of a criterion for semistable vector bundles
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