Prisms, prismatic neighborhoods, and p-de Rham cohomology
By Arthur Ogus
Prismatic cohomology, as proposed by B. Bhatt and P. Scholze, provides a uniform framework for many of the cohomoogy theories involved in p-adic Hodge theory. I will focus on the crystalline incarnation of prismatic cohomology and its relation to p-de Rham cohomology, as suggested by B. Bhatt. I will also attempt to relate crystalline prisms to previoius work on the p-adic Cartier transform due to several authors. The main new ingredient is a detailed study of the geometry of Frobenius lifts and prismatic neighborhoods.