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

Biswas, Indranil1 ; Holla, Yogish I.1 ; Parameswaran, A.J.1 ; Subramanian, S.1
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Comptes Rendus. Mathématique, Tome 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
Biswas, Indranil 1 ; Holla, Yogish I. 1 ; Parameswaran, A.J. 1 ; Subramanian, S. 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 
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     title = {Construction of a {Frobenius} nonsplit {Harder{\textendash}Narasimhan} filtration},
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Biswas, Indranil; Holla, Yogish I.; Parameswaran, A.J.; Subramanian, S. Construction of a Frobenius nonsplit Harder–Narasimhan filtration. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 545-548. doi : 10.1016/j.crma.2008.03.011. http://www.numdam.org/articles/10.1016/j.crma.2008.03.011/

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

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

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