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 -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 -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 -degeneration theorem due to Cattani-Kaplan-Schmid and Kashiwara-Kawai, and the vanishing theorem of Saito for VHSs of geometric origin.
Cite
@article{arxiv.1904.06651,
title = {Intersection de Rham complexes in positive characteristic},
author = {Mao Sheng and Zebao Zhang},
journal= {arXiv preprint arXiv:1904.06651},
year = {2023}
}
Comments
Third version. Replace the second version entitled 'On the decomposition theorem for intersection de Rham complexes'. 42 pages. Comments are greatly appreciated