Comptes Rendus
no. 9-10
Algebraic Geometry
Construction of a Frobenius nonsplit Harder–Narasimhan filtration
[Construction d'une filtration de Harder–Narasimhan Frobenius non-scindée]

Présenté par : Michel Raynaud

Indranil Biswas1 ; Yogish I. Holla1 ; A.J. Parameswaran1 ; S. Subramanian1
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 545-548.

Nous construisons un exemple de fibré vectoriel V au-dessus d'une variété projective lisse X tel que, pour tout n⩾1, la filtration de Harder–Narasimhan de FXnV, où FX est le morphisme de Frobenius de X, est non-scindée.

We construct an example of a vector bundle V over a smooth projective variety X such that for no n⩾1, the Harder–Narasimhan filtration of FXnV splits, where FX is the Frobenius morphism of X.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.03.011
Indranil Biswas 1 ; Yogish I. Holla 1 ; A.J. Parameswaran 1 ; S. Subramanian 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 
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     author = {Indranil Biswas and Yogish I. Holla and A.J. Parameswaran and S. Subramanian},
     title = {Construction of a {Frobenius} nonsplit {Harder{\textendash}Narasimhan} filtration},
     journal = {Comptes Rendus. Math\'ematique},
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Indranil Biswas; Yogish I. Holla; A.J. Parameswaran; S. Subramanian. Construction of a Frobenius nonsplit Harder–Narasimhan filtration. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 545-548. doi : 10.1016/j.crma.2008.03.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.011/

[1] I. Biswas; A.J. Parameswaran On the ample vector bundles over curves in positive characteristic, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 355-358

[2] L. Illusie; M. Raynaud Les suites spectrales associées au complexe de de Rham–Witt, Inst. Hautes Études Sci. Publ. Math., Volume 57 (1983), pp. 73-212

[3] A. Langer Semistable sheaves in positive characteristic, Ann. of Math., Volume 159 (2004), pp. 251-276

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