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Generalization of a criterion for semistable vector bundles | | Indranil Biswas
; Georg Hein
; | | Date: |
25 Apr 2008 | | 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 $F$. | | Source: | arXiv, 0804.4120 | | Services: | Forum | Review | PDF | Favorites | |
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