Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semistability of Frobenius direct images over curves   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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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th