Algebraic Geometry
Construction of a Frobenius nonsplit Harder–Narasimhan filtration
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 545-548.

We construct an example of a vector bundle V over a smooth projective variety X such that for no n1, the Harder–Narasimhan filtration of FXnV splits, where FX is the Frobenius morphism of X.

Nous construisons un exemple de fibré vectoriel V au-dessus d'une variété projective lisse X tel que, pour tout n1, la filtration de Harder–Narasimhan de FXnV, où FX est le morphisme de Frobenius de X, est non-scindée.

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Accepted:
Published online:
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, Volume 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/

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[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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