Construction of a Frobenius nonsplit Harder-Narasimhan filtration

Abstract 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 . To cite this article: I. Biswas et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).