An explicit infinite homotopy in nonabelian Hodge theory in positive characteristic

TL;DR

This paper provides an explicit infinite homotopy connecting Higgs complexes to Frobenius pushforwards of de Rham complexes in positive characteristic, advancing understanding in nonabelian Hodge theory.

Contribution

It offers detailed verification of an explicit infinite homotopy in nonabelian Hodge theory in positive characteristic, previously outlined without proof.

Findings

Explicit construction of the homotopy is verified.

Bridges Higgs complexes and Frobenius pushforwards.

Enhances the theoretical framework in positive characteristic.

Abstract

This short note is extracted from Section 3 and Appendix of the paper entitled with Intersection de Rham complexes in positive characteristic by the same named authors, where an explicit infinite homotopy from a Higgs complex to the Frobenius pushforward of the corresponding de Rham complex in positive characteristic has been provided. The verification details, which are omitted therein, are provided here.