Semistability of Frobenius direct images over curves

Vikram Mehta , Christian Pauly (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 $X$.

Domaines: Géométrie algébrique [math.AG]

Vikram Mehta, Christian Pauly. Semistability of Frobenius direct images over curves. 2006. ⟨hal-00087308⟩