3 papers
math.AG2023
Tilting and untilting for ideals in perfectoid rings
Dimitri Dine, Ryo Ishizuka
For an (integral) perfectoid ring of characteristic with tilt , we introduce and study a tilting map from the set of -adically closed ideals of…
math.AC2023
A calculation of the perfectoidization of semiperfectoid rings
Ryo Ishizuka
We show that perfectoidization can be (almost) calculated by using -root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of…
math.AC2023
A mixed characteristic analogue of the perfection of rings and its almost Cohen-Macaulay property
Ryo Ishizuka, Kazuma Shimomoto
Over a complete Noetherian local domain of mixed characteristic with perfect residue field, we construct a perfectoid ring which is similar to an explicit representation of a perfe…