no. 4
Algebraic geometry
The stability of Frobenius direct images of rank-two bundles over surfaces
[La stabilité de l'image directe de Frobenius des fibrés de rang deux sur des surfaces]
Présenté par : Claire Voisin
Liu, Congjun1 ; Zhou, Mingshuo2
1 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
2 School of Science, Hangzhou Dianzi University, Hangzhou 310018, PR China
Comptes Rendus. Mathématique, Tome 353 (2015) no. 4, pp. 339-344

Let X be a smooth projective surface over an algebraically closed field k of characteristic p≥5 with ΩX1 semistable and μ(ΩX1)>0. Given a semistable (resp. stable) vector bundle W of rank 2, we prove that the direct image F⁎W under the Frobenius morphism F is also semistable (resp. stable).

Soit X une surface projective lisse sur un corps algébriquement clos k de caractéristique p≥5 avec ΩX1 semistable et μ(ΩX1)>0. Étant donné un fibré vectoriel semistable (resp. stable) W de rang 2 sur X, on montre que l'image directe F⁎W par le morphisme de Frobenius F est aussi semistable (resp. stable).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.12.001

Liu, Congjun 1 ; Zhou, Mingshuo 2

1 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
2 School of Science, Hangzhou Dianzi University, Hangzhou 310018, PR China 
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Liu, Congjun; Zhou, Mingshuo. The stability of Frobenius direct images of rank-two bundles over surfaces. Comptes Rendus. Mathématique, Tome 353 (2015) no. 4, pp. 339-344. doi: 10.1016/j.crma.2014.12.001

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