Dans cette courte note, nous donnons des exemples explicites en caracteristique p sur certaines courbes projectives lisses où, pour un fibré vectoriel semi-stable donné , la longeur de la filtration d'Harder–Narasimhan de est plus grande que p. Cela répond negativement à une question posée par Mehta et Pauly dans [2].
In this short note, we provide explicit examples in characteristic p on certain smooth projective curves where for a given semistable vector bundle the length of the Harder–Narasimhan filtration of is longer than p. This negatively answers a question of Mehta and Pauly raised in [2].
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@article{CRMATH_2015__353_9_855_0, author = {Brenner, Holger and St\"abler, Axel}, title = {On a question of {Mehta} and {Pauly}}, journal = {Comptes Rendus. Math\'ematique}, pages = {855--857}, publisher = {Elsevier}, volume = {353}, number = {9}, year = {2015}, doi = {10.1016/j.crma.2015.06.007}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.06.007/} }
TY - JOUR AU - Brenner, Holger AU - Stäbler, Axel TI - On a question of Mehta and Pauly JO - Comptes Rendus. Mathématique PY - 2015 SP - 855 EP - 857 VL - 353 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.06.007/ DO - 10.1016/j.crma.2015.06.007 LA - en ID - CRMATH_2015__353_9_855_0 ER -
Brenner, Holger; Stäbler, Axel. On a question of Mehta and Pauly. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 855-857. doi : 10.1016/j.crma.2015.06.007. http://archive.numdam.org/articles/10.1016/j.crma.2015.06.007/
[1] On Frobenius-destabilized rank-2 vector bundles over curves, Comment. Math. Helv., Volume 83 (2008), pp. 179-209
[2] Semistability of Frobenius direct images over curves, Bull. Soc. Math. Fr., Volume 135 (2007) no. 1, pp. 105-117
[3] Direct images of bundles under Frobenius morphism, Invent. Math., Volume 173 (2008) no. 173, pp. 427-447
[4] The H-N filtration of bundles as Frobenius pull-back, 2012 (preprint) | arXiv
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