We construct an example of a vector bundle V over a smooth projective variety X such that for no , the Harder–Narasimhan filtration of splits, where 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 , la filtration de Harder–Narasimhan de , où est le morphisme de Frobenius de X, est non-scindée.
Accepted:
Published online:
Indranil Biswas 1; Yogish I. Holla 1; A.J. Parameswaran 1; S. Subramanian 1
@article{CRMATH_2008__346_9-10_545_0, 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}, }
TY - JOUR AU - Indranil Biswas AU - Yogish I. Holla AU - A.J. Parameswaran AU - S. Subramanian TI - Construction of a Frobenius nonsplit Harder–Narasimhan filtration JO - Comptes Rendus. Mathématique PY - 2008 SP - 545 EP - 548 VL - 346 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2008.03.011 LA - en ID - CRMATH_2008__346_9-10_545_0 ER -
%0 Journal Article %A Indranil Biswas %A Yogish I. Holla %A A.J. Parameswaran %A S. Subramanian %T Construction of a Frobenius nonsplit Harder–Narasimhan filtration %J Comptes Rendus. Mathématique %D 2008 %P 545-548 %V 346 %N 9-10 %I Elsevier %R 10.1016/j.crma.2008.03.011 %G en %F CRMATH_2008__346_9-10_545_0
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/
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[3] Semistable sheaves in positive characteristic, Ann. of Math., Volume 159 (2004), pp. 251-276
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