Direct images of bundles under Frobenius morphism

By Xiaotao Sun. 2006

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Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k)=p>0 and F:X→X1 be the relative Frobenius morphism. For any vector bundle W on X, we prove that instability of F*W is bounded by instability of W⊗Tℓ(Ω1X) (0≤ℓ≤n(p-1)) (Corollary 4.9). When X is a smooth projective curve of genus g≥2, it implies F*W being stable whenever W is stable.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

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