Let X be a geometrically irreducible smooth projective curve defined over a field k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that for . We give an explicit bound for the rank of F. The proof uses a result of Popa for the case where k is algebraically closed.
Soit X une courbe projective lisse géométriquement irréductible définie sur un corps k, et soit E un fibré vectoriel sur X. E est semi-stable si et seulement s'il y a un fibré vectoriel F sur X tel que pour . Nous donnons une borne explicite pour le rang de F. La preuve utilise un résultat de Popa pour le cas où k est algébriquement clos.
Accepted:
Published online:
Indranil Biswas 1; Georg Hein 2; Norbert Hoffmann 3
@article{CRMATH_2008__346_17-18_981_0, author = {Indranil Biswas and Georg Hein and Norbert Hoffmann}, title = {On semistable vector bundles over curves}, journal = {Comptes Rendus. Math\'ematique}, pages = {981--984}, publisher = {Elsevier}, volume = {346}, number = {17-18}, year = {2008}, doi = {10.1016/j.crma.2008.07.016}, language = {en}, }
Indranil Biswas; Georg Hein; Norbert Hoffmann. On semistable vector bundles over curves. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 981-984. doi : 10.1016/j.crma.2008.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.016/
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