Intersection de Rham complexes in positive characteristic

Abstract

We establish a positive characteristic analogue of intersection cohomology theory for variations of Hodge structure. It includes: a) the de Rham-Higgs comparison theorem for the intersection de Rham complex; b) the $E_1$-degeneration theorem for the intersection de Rham complex of a periodic de Rham bundle; c) the Kodaira-Saito vanishing theorem for the intersection cohomology groups of a periodic Higgs bundle. These results generalize the decomposition theorem of Deligne-Illusie and the de Rham-Higgs theorem of Ogus-Vologodsky, the $E_1$-degneration theorem of Deligne-Illusie, Illusie, Faltings and the Kodaira-Saito vanishing theorem of Arapura. As an application, we give an algebraic proof of the $E_1$-degeneration theorem due to Cattani-Kaplan-Schmid and Kashiwara-Kawai, and the vanishing theorem of Saito for VHSs of geometric origin.

Third version. Replace the second version entitled 'On the decomposition theorem for intersection de Rham complexes'. 42 pages. Comments are greatly appreciated

References in corpus (2)

• Logarithmic nonabelian Hodge theory in characteristic p
• Nonabelian Hodge theory in positive characterstic via exponential twisting

Cited by in corpus (2)

• Periodic de Rham bundles over curves
• A note on the filtered decomposition theorem