Algebraicity in monochromatic homotopy theory

Using Patchkoria--Pstr{a}gowski's version of Franke's algebraicity theorem, we prove that the category of Kₚ(n)-local spectra is exotically equivalent to the category of derived Iₙ-complete periodic comodules over the Adams Hopf algebroid (E_*, E_*E) for large primes. This gives a finite prime result analogous to the asymptotic algebraicity for SpKₚ(n) of Barthel--Schlank--Stapleton.