Abstract
We introduce the notion of a 𝑝-Cartier smooth algebra. It generalises that of a smooth algebra and includes valuation rings over a perfectoid base. We give several characterisations of 𝑝-Cartier smoothness in terms of prismatic cohomology and deduce a comparison theorem between syntomic and étale cohomologies under this hypothesis.
Funding source: H2020 European Research Council
Award Identifier / Grant number: 101001474
Funding statement: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001474).
Acknowledgements
I am very grateful to Matthew Morrow for suggesting this project to me, sharing many insights and for careful readings of this manuscript. I would also like to thank Elden Elmanto and Arnab Kundu for helpful discussions, Javier Fresán, Akhil Mathew and Mohamed Moakher for comments on a draft of this paper, and the referee for many helpful comments and corrections.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A non-Archimedean approach to K-stability, II: Divisorial stability and openness
- Uniqueness of asymptotically conical higher codimension self-shrinkers and self-expanders
- A Schur’s theorem via a monotonicity and the expansion module
- On Waring’s problem for larger powers
- Tangent flows of Kähler metric flows
- Ramified covers of abelian varieties over torsion fields
- Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
- Cartier smoothness in prismatic cohomology
Articles in the same Issue
- Frontmatter
- A non-Archimedean approach to K-stability, II: Divisorial stability and openness
- Uniqueness of asymptotically conical higher codimension self-shrinkers and self-expanders
- A Schur’s theorem via a monotonicity and the expansion module
- On Waring’s problem for larger powers
- Tangent flows of Kähler metric flows
- Ramified covers of abelian varieties over torsion fields
- Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
- Cartier smoothness in prismatic cohomology