A graded absolute perfectoidization is built for G-graded adic rings, with the key result that the absolute perfectoidization of the structure sheaf on projective-type formal schemes algebraizes.
Mathew , The Galois Group of a Stable Homotopy Theory , Advances in Mathematics , 291 ( 2016 ) 403 -- 541
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Algebraization of absolute perfectoidization via section rings
A graded absolute perfectoidization is built for G-graded adic rings, with the key result that the absolute perfectoidization of the structure sheaf on projective-type formal schemes algebraizes.