Abstract

Prismatic theory, introduced by Bhatt and Scholze, has provided a new framework for integral p-adic Hodge theory and arithmetic geometry. This mini-course aims to give an accessible introduction to prismatic theory and explore its applications to p-adic local systems and deformation theory. 

 

In the first two lectures, we will introduce the absolute (log) prismatic site and prismatic F-crystals. We will present our recent works on the classification of crystalline and semistable Z_p-local systems using analytic (log) prismatic F-crystals. We will also discuss several realization functors, including étale, crystalline, and shtuka realization functors, as well as a prismatic purity theorem for semistable local systems.

 

References: 

B. Bhatt and P. Scholze, Prisms and prismatic cohomology. 

H. Du, T. Liu, Y. S. Moon, and K. Shimizu, Completed prismatic F-crystals and crystalline Z_p-local systems. 

H. Du, T. Liu, Y. S. Moon, and K. Shimizu, Log prismatic F-crystals and purity. 

K. Ito, Deformation theory for prismatic G-displays. 

N. Imai, H. Kato, and A. Youcis, The prismatic realization functor for Shimura varieties of abelian type.

 

Organizer

Chia-Fu Yu( Academia Sinica)