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. 

 

Organizer

Chia-Fu Yu, Academia Sinica