Semistability of Frobenius direct images over curves
Copyright policy )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 $X$.
8 pages
Mathematics - Algebraic Geometry, Algebraic moduli problems, moduli of vector bundles, 14H40, 14D20, Frobenius, FOS: Mathematics, semistability, Jacobians, Prym varieties, vector bundle, Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, Algebraic moduli problems, moduli of vector bundles, 14H40, 14D20, Frobenius, FOS: Mathematics, semistability, Jacobians, Prym varieties, vector bundle, Algebraic Geometry (math.AG)
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