Algebraic Geometry
Stable bundles as Frobenius morphism direct image
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 381-383.

Let X be a smooth projective curve of genus g2 over an algebraically closed field k of characteristic p>0, and let F:XX1 be the relative Frobenius morphism. We show that a vector bundle E on X1 is the direct image under F of some stable bundle on X if and only if the instability of FE is equal to (p1)(2g2).

Soient X une courbe projective lisse de genre g2 définie sur un corps k algébriquement clos de caractéristique p>0, et F:XX1 le morphisme de Frobenius relatif. On montre quʼun fibré vectoriel E sur X1 est lʼimage directe sous F dʼun certain fibré stable sur X si et seulement si lʼinstabilité de FE est égale à (p1)(2g2).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.04.021
Liu, Congjun 1; Zhou, Mingshuo 1

1 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PR China
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Liu, Congjun; Zhou, Mingshuo. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.04.021/

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