Construction of a Frobenius nonsplit Harder–Narasimhan filtration

Indranil Biswas; Yogish I. Holla; A.J. Parameswaran; S. Subramanian

doi:10.1016/j.crma.2008.03.011

Algebraic Geometry

Construction of a Frobenius nonsplit Harder–Narasimhan filtration

Presented by: Michel Raynaud

Indranil Biswas ¹; Yogish I. Holla ¹; A.J. Parameswaran ¹; S. Subramanian ¹

¹School 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

Abstract (Original language)
Résumé

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 $F_{X}^{n} V$ splits, where $F_{X}$ 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 $n ⩾ 1$ , la filtration de Harder–Narasimhan de $F_{X}^{n} V$ , où $F_{X}$ est le morphisme de Frobenius de X, est non-scindée.

Received: 2008-02-06
Accepted: 2008-03-11
Published online: 2008-04-11

DOI: 10.1016/j.crma.2008.03.011

Author's affiliations:

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},
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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

References
Cited by

[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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