Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings

Abstract

To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants and finiteness properties. Using this, we also provide a comparison result on étale cohomology groups under the tilting. As an application, we prove finiteness of the prime-to-$p$-torsion subgroup of the divisor class group of a local log-regular ring that appears in logarithmic geometry in the mixed characteristic case.

Final version accepted by Algebra and Number Theory

References in corpus (2)

• Relative vanishing theorems for $\mathbf{Q}$-schemes
• Local log-regular rings vs. toric rings

Cited by in corpus (2)

• Prismatic Kunz's theorem
• Perfectoid towers generated from prisms