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Frobenius pull backs of vector bundles in higher dimensions

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Abstract

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 destabilizing 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 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 of X.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India

    V TRIVEDI

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  1. V TRIVEDI
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TRIVEDI, V. Frobenius pull backs of vector bundles in higher dimensions. Proc Math Sci 122, 615–628 (2012). https://doi.org/10.1007/s12044-012-0097-0

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  • DOI: https://doi.org/10.1007/s12044-012-0097-0

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