Abstract
Let \(X\) be a smooth projective surface over an algebraically closed field \(k\) of characteristic \(p > 0\) with \({\Omega _{X}^{1}}\) semistable and \(\mu ({\Omega _{X}^{1}})>0\). For any semistable (resp. stable) bundle \(W\) of rank \(r\), we prove that \(F_*W\) is semistable (resp. stable) when \(p\ge r(r-1)^2+1\).
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Acknowledgments
The authors would like to thank the Professor Xiaotao Sun for careful reading of this manuscript and for helpful comments, which improve the paper both in mathematics and presentations. The authors are also grateful to the anonymous referees for numerous suggestions that helped make this paper more readable.
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Liu, C., Zhou, M. Stability of Frobenius direct images over surfaces. Math. Z. 280, 841–850 (2015). https://doi.org/10.1007/s00209-015-1451-6
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DOI: https://doi.org/10.1007/s00209-015-1451-6