Prismatic Kunz's theorem

Abstract

In this paper, we prove "prismatic Kunz's theorem" which states that a complete Noetherian local ring $R$ of residue characteristic $p$ is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) $R$ over a specific prism $(A,I)$ is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the "Frobenius map" to mixed characteristic rings. Our approach involves studying the deformation problem of the "regularity" of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex.

31 pages; accepted in J.Algebra

References in corpus (2)

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

Cited by in corpus (1)

• Perfectoid towers generated from prisms