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- W2951516998 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 the cohomologies of Eotimes 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 Eotimes F vanish. We also give an explicit bound for the rank of $F$." @default.
- W2951516998 created "2019-06-27" @default.
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- W2951516998 date "2008-04-25" @default.
- W2951516998 modified "2023-09-27" @default.
- W2951516998 title "Generalization of a criterion for semistable vector bundles" @default.
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