4 papers · 1 filter
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…
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 …
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…