A Note on the Filtered Decomposition Theorem

Abstract

We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version. There are two applications. The easier one provides a mod p proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a positive characteristic analogue of a theorem of Deligne on the mixed Hodge structure attached to complex algebraic varieties.

Keywords

Decomposition theorem / Mixed Fontaine–Laffaille complex / Spectral sequence / Vanishing theorem / Weight filtration