The method of perfectoidization was introduced by Bhatt-Scholze as a mixed characteristic analogue of the perfection of rings of positive characteristic.
This talk aims to explain the realization of the perfectoidization of semiperfectoid rings by means of the application of $p$-root closure, a commutative algebraic construction investigated by P. Roberts in the context of mixed characteristic commutative algebra. Time permitting, we will talk about our recent research about prismatic complexes.

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