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Semistability of Frobenius direct images over curves

Vikram Mehta·Christian Pauly
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Abstract

Let $X$ be a smooth projective curve of genus $g \geq 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Given a semistable vector bundle $E$ over $X$, we show that its direct image $F\_*E$ under the Frobenius map $F$ of $X$ is again semistable. We deduce a numerical characterization of the stable rank-$p$ vector bundles $F\_*L$, where $L$ is a line bundle over $X$.

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Vikram Mehta, Christian Pauly. 2006-07-22. Semistability of Frobenius direct images over curves. https://arxiv.org/abs/math/0607565

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