Generalization of a criterion for semistable vector bundles
Indranil Biswas, Georg Hein
Number | 27 |
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Author | Georg Hein |
Project | C10 |
Year | 2008 |
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 H0(X,E⊗F) and H1(X,E⊗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 Hi(X,E⊗F)=0 for all i. We also give an explicit bound for the rank of F.