Conference on Arithmetic Geometry in honor of Luc Illusie

Collection Conference on Arithmetic Geometry in honor of Luc Illusie

Organizer(s) Lei Fu (Tsinghua University), Fabrice Orogozo (CNRS&IMJ-PRG), Weizhe Zheng (MCM, AMSS, CAS)
Date(s) 6/7/21 - 6/11/21
00:00:00 / 00:00:00
4 22

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.

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