4 papers
Structural properties and tilting correspondences of perfectoid towers
Kazuki Hayashi
We prove that every perfectoid tower can be realized as the fiber product of a diagram involving perfectoid towers that are either -torsion free or perfect of characteristic …
Regular rings and perfectoid towers
Kazuki Hayashi
We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic is regular if and only if it admits…
A characterization of perfectoid towers in terms of conormal cones
Kazuki Hayashi
We characterize perfectoid towers in terms of conormal cones rather than torsion parts. This result is deduced from a refined study of the relationship between torsion with respect…
An application of Fontaine's monoidal maps to perfectoid towers
Kazuki Hayashi, Shinnosuke Ishiro, Kazuma Shimomoto
To connect arithmetic and ring-theoretic properties of rings of mixed characteristic with those of positive characteristic, we introduce monoidal maps for perfectoid towers. Using…