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
[Construction d'une filtration de Harder–Narasimhan Frobenius non-scindée]

Présenté par : Michel Raynaud

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

Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 545-548.

Résumé
Abstract

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.

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.

Reçu le : 2008-02-06
Accepté le : 2008-03-11
Publié le : 2008-04-11

DOI : 10.1016/j.crma.2008.03.011

Affiliations des auteurs :

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},
     pages = {545--548},
     publisher = {Elsevier},
     volume = {346},
     number = {9-10},
     year = {2008},
     doi = {10.1016/j.crma.2008.03.011},
     language = {en},
}

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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/

Bibliographie
Cité par

[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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