Algebraicity in monochromatic homotopy theory

Using Patchkoria--Pstragowski'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 Sp₊䂹 (₍) of Barthel--Schlank--Stapleton.