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A Characterization of Ordinary Abelian Varieties by the Frobenius Push-Forward of the Structure Sheaf II
Abstract In this paper, we prove that a smooth projective variety X of characteristic p > 0 is an ordinary abelian variety if and only if KX is pseudo-effective and $F_{*}^{e}{\mathcal {O}}_{X}$ splits into a direct sum of line bundles for an integer e with pe > 2.