no. 9-10
Algebraic Geometry
Stable bundles as Frobenius morphism direct image
[Faisceaux stables en tant quʼimages directes par le morphisme de Frobenius]
Présenté par : Claire Voisin
Liu, Congjun1 ; Zhou, Mingshuo1
1 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PR China
Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 381-383

Let X be a smooth projective curve of genus g⩾2 over an algebraically closed field k of characteristic p>0, and let F:X→X1 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 F⁎E is equal to (p−1)(2g−2).

Soient X une courbe projective lisse de genre g⩾2 définie sur un corps k algébriquement clos de caractéristique p>0, et F:X→X1 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 F⁎E est égale à (p−1)(2g−2).

Reçu le :
Accepté le :
Publié le :
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, Tome 351 (2013) no. 9-10, pp. 381-383. doi: 10.1016/j.crma.2013.04.021

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