A correspondence is shown between lim-perfectoid splitting of projective schemes and lim-perfectoid purity of their Gorenstein section rings, supplying new examples of lim-perfectoid pure rings.
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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.
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A local-global correspondence for perfectoid purity
A correspondence is shown between lim-perfectoid splitting of projective schemes and lim-perfectoid purity of their Gorenstein section rings, supplying new examples of lim-perfectoid pure rings.
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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.