Name
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 both H^0(X,E@?F) and H^1(X,E@?F) vanishes. 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 H^i(X,E@?F)=0 for all i. We also give an explicit bound for the rank of F. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.ffa.2009.06.001 | Finite Fields and Their Applications |
Keywords | Field | DocType |
vector bundle,vector bundle e,vector bundle f,smooth projective curve y,geometrically irreducible smooth projective,perfect field k,semistable vector bundle,perfect field,algebraic geometry,moduli space | Section (fiber bundle),Combinatorics,Normal bundle,Vector bundle,Tautological line bundle,Frame bundle,Line bundle,Principal bundle,Mathematics,Vector-valued differential form | Journal |
Volume | Issue | ISSN |
15 | 5 | 1071-5797 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Indranil Biswas | 1 | 9 | 3.26 |
| Georg Hein | 2 | 0 | 0.34 |