A de Rham-Higgs comparison for mixed-Hodge-module-inspired subcomplexes is established in special positive-characteristic cases, yielding decomposition and vanishing theorems when the logarithmic cotangent bundle splits into small-rank subbundles.
An explicit infinite homotopy in nonabelian Hodge theory in positive characteristic
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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.
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De Rham-Higgs comparison for mixed Hodge modules in positive characteristic
A de Rham-Higgs comparison for mixed-Hodge-module-inspired subcomplexes is established in special positive-characteristic cases, yielding decomposition and vanishing theorems when the logarithmic cotangent bundle splits into small-rank subbundles.