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

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

2011-10-12

arxiv.org/abs/1110.2567v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

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 Koll\'ar 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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