Prisms and prismatic cohomology
By B. Bhatt, Peter Scholze. Annals of Mathematics, 2019
237 citations recorded by the source corpus.
We introduce the notion of a prism, which may be regarded as a "deperfection" of the notion of a perfectoid ring. Using prisms, we attach a ringed site --- the prismatic site --- to a $p$-adic formal scheme. The resulting cohomology theory specializes to (and often refines) most known integral $p$-adic cohomology theories. As applications, we prove an improved version of the almost purity theorem allowing ramification along arbitrary closed subsets (without using adic spaces), give a co-ordinate free description of $q$-de Rham cohomology as conjectured by the second author, and settle a vanishing conjecture for the $p$-adic Tate twists $\mathbf{Z}_p(n)$ introduced in previous joint work with Morrow.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/de729843ecf86f57d58ed0c728b977e98ccf8a57
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The prismatization of $p$-adic formal schemes (2022, methodology): “22), justifying the name “animated δ-ring”; the latter approach is the one adopted in other places, such as [17] and also implicitly in various arguments of [3].”