The authors develop twisting of Higgs modules via Higgs-Tate algebras that extends the p-adic Simpson correspondence to arbitrary pullbacks and proper (log)smooth direct images while recovering prior constructions as special cases.
Serre, Cohomologie galoisienne, Cinquième édition révisée et complétée, Lecture Notes in Math.5, Springer-Verlag (1997)
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Twisting Higgs Modules and Functorial Aspects of the p-adic Simpson Correspondence
The authors develop twisting of Higgs modules via Higgs-Tate algebras that extends the p-adic Simpson correspondence to arbitrary pullbacks and proper (log)smooth direct images while recovering prior constructions as special cases.