De Rham-Higgs comparison for mixed Hodge modules in positive characteristic

TL;DR

This paper extends the nonabelian Hodge theory in positive characteristic to a mixed Hodge module framework, generalizing the decomposition theorem of Deligne and Illusie, with verification in specific cases and new byproducts.

Contribution

It introduces a novel generalization of the decomposition theorem for mixed Hodge modules in positive characteristic, building on prior nonabelian Hodge theory developments.

Findings

Verification of the generalized decomposition theorem in special cases

Extension of Sheng's method to new contexts

Derivation of several interesting byproducts

Abstract

Building on the nonabelian Hodge theory in positive characteristic developed by Ogus, Vologodsky, and Schepler, we propose a generalization of the decomposition theorem of Deligne and Illusie from the perspective of mixed Hodge modules. This generalization is verified in certain special cases by extending the method of Sheng and the author, leading to several interesting byproducts.