Cartier smoothness in prismatic cohomology

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.

v2: minor updates, some proofs are simplified

Cited by in corpus (1)

• Syntomic complexes and $p$-adic étale Tate twists