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    Decomposition of De Rham Complexes with Smooth Horizontal Coefficients for Semistable Reductions

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    We generalize Illusie's result to prove the decomposition of the de Rham complex with smooth horizontal coefficients for a semistable SS-morphism f:X\ra Y which is liftable over Z/p2Z\Z/p^2\Z. As an application, we prove the Koll\'ar vanishing theorem in positive characteristic for a semistable SS-morphism f:X\ra Y which is liftable over Z/p2Z\Z/p^2\Z, where all concerned horizontal divisors are smooth over YY.Comment: 26 page
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