Stability of Frobenius direct images over surfaces

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 $F_{\ast }W$ is semistable (resp. stable) when $p\ge r(r-1{)}^2+1$.

10 pages

References in corpus (1)

• Direct images of bundles under Frobenius morphisms