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arXiv · 1110.2567

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

Qihong Xie
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Abstract

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

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Qihong Xie. 2011-10-12. Decomposition of De Rham Complexes with Smooth Horizontal Coefficients for Semistable Reductions. https://arxiv.org/abs/1110.2567

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