Structural properties and tilting correspondences of perfectoid towers

2026/05/31 by Kazuki Hayashi · 2 citations
Mathematics · #math.AC #math.AG #math.NT #msc:14G45 #msc:13B02

paper · pdf

31 pages

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

We prove that every perfectoid tower can be realized as the fiber product of a diagram involving perfectoid towers that are either p-torsion free or perfect of characteristic p. As an application, we conclude that separated perfectoid towers are reduced. We also establish the tilting invariance of Koszul homology for perfectoid towers. As further applications, we prove that tilting preserves fundamental properties of Noetherian local rings such as being Cohen--Macaulay, Gorenstein, complete intersection, or regular.

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