Stability of direct images under Frobenius morphism

arXivmath/0608043MaRDI QIDQ6477622

Xiaotao Sun

Publication date: 1 August 2006

Abstract: Let $X$ be a smooth projective variety over an algebraically field $k$ with $mchar(k)=p>0$ and $F:Xo{X}_1$ be the relative Frobenius morphism. When $mdim(X)=1$, we prove that $F_{*}W$ is a stable bundle for any stable bundle $W$ (Theorem ef{thm1.3}). As a step to study the question for higher dimensional $X$, we generalize the canonical filtration (defined by Joshi-Ramanan-Xia-Yu for curves) to higher dimensional $X$ (Theorem ef{thm2.6}).

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