Stable bundles as Frobenius morphism direct image

Liu, Congjun; Zhou, Mingshuo

doi:10.1016/j.crma.2013.04.021

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, Congjun ¹ ; Zhou, Mingshuo ¹

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.

Résumé
Abstract

Soient X une courbe projective lisse de genre $g ⩾ 2$ définie sur un corps k algébriquement clos de caractéristique $p > 0$ , et $F : X \to X_{1}$ le morphisme de Frobenius relatif. On montre quʼun fibré vectoriel E sur $X_{1}$ est lʼimage directe sous F dʼun certain fibré stable sur X si et seulement si lʼinstabilité de $F^{⁎} E$ est égale à $(p - 1) (2 g - 2)$ .

Let X be a smooth projective curve of genus $g ⩾ 2$ over an algebraically closed field k of characteristic $p > 0$ , and let $F : X \to X_{1}$ be the relative Frobenius morphism. We show that a vector bundle E on $X_{1}$ is the direct image under F of some stable bundle on X if and only if the instability of $F^{⁎} E$ is equal to $(p - 1) (2 g - 2)$ .

Reçu le : 2013-01-27
Accepté le : 2013-04-26
Publié le : 2013-05-01

DOI : 10.1016/j.crma.2013.04.021

Affiliations des auteurs :

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. http://www.numdam.org/articles/10.1016/j.crma.2013.04.021/

Bibliographie
Cité par

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[3] Mehta, V.; Pauly, C. Semistability of Frobenius direct images over curves, Bull. Soc. Math. Fr., Volume 135 (2007), pp. 105-117

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[5] Sun, X. Direct images of bundles under Frobenius morphism, Invent. Math., Volume 173 (2008), pp. 427-447

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