Vladimir Shein, December 1, 2023

Abstract.   Prismatization is a functor from the category of bounded p-adic formal schemes to stacks over \(\mathbb{Z}_p\). Cohomology of the structure sheaf of the stack corresponding to a scheme \(X\) is prismatic cohomology of \(X\), which can specialize into étale, de-Rham, or crystalline cohomology of \(X\).

In the first part of the talk, I will recall the necessary definitions and some classical results. Then I will explain the construction of the prismatization functor and define prismatic cohomology. If time permits, I will discuss the connection of prismatic cohomology to other cohomology theories.