Let X be a smooth projective curve of genus over an algebraically closed field k of characteristic , and let be the relative Frobenius morphism. We show that a vector bundle E on is the direct image under F of some stable bundle on X if and only if the instability of is equal to .
Soient X une courbe projective lisse de genre définie sur un corps k algébriquement clos de caractéristique , et le morphisme de Frobenius relatif. On montre quʼun fibré vectoriel E sur est lʼimage directe sous F dʼun certain fibré stable sur X si et seulement si lʼinstabilité de est égale à .
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Congjun Liu 1; Mingshuo Zhou 1
@article{CRMATH_2013__351_9-10_381_0, author = {Congjun Liu and Mingshuo Zhou}, title = {Stable bundles as {Frobenius} morphism direct image}, journal = {Comptes Rendus. Math\'ematique}, pages = {381--383}, publisher = {Elsevier}, volume = {351}, number = {9-10}, year = {2013}, doi = {10.1016/j.crma.2013.04.021}, language = {en}, }
Congjun Liu; Mingshuo Zhou. Stable bundles as Frobenius morphism direct image. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 381-383. doi : 10.1016/j.crma.2013.04.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.021/
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