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- W2952329068 abstract "Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of the Frobenius pull-back of the Harder-Narasimhan filtration of $E$, provided there is a lower bound on the characteristic $p$ (in terms of rank of $E$ and the slope of the destabilising sheaf of the cotangent bundle of $X$). We also recall some examples, due to Raynaud and Monsky,to show that some lower bound on $p$ is necessary. We further prove an analogue of this result for principal $G$-bundles over $X$. We also give a bound on the instability degree of the Frobenius pull back of $E$ in terms of the instability degree of $E$ and well defined invariants ot $X$ and $E$." @default.
- W2952329068 created "2019-06-27" @default.
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- W2952329068 date "2010-11-08" @default.
- W2952329068 modified "2023-09-25" @default.
- W2952329068 title "Frobenius pull backs of vector bundles in higher dimensions" @default.
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- W2952329068 doi "https://doi.org/10.48550/arxiv.1011.1971" @default.
- W2952329068 hasPublicationYear "2010" @default.
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