Introduction to Prismatic cohomology

Record: No

Level: Graduate

Language: English

Prerequisite

Algebraic geometry (background in algebraic number theory will be helpful)

Abstract

Prismatic cohomology, which is developed in a recent work of Bhatt-Scholze, is a cohomology theory for schemes over p-adic rings. It is considered to be an overarching cohomology theory in p-adic geometry, unifying etale, de Rham, and crystalline cohomology. Due to wide-ranging applications in p-adic Hodge theory and p-adic Galois representations, it is one of the central topics of active research. In this course, we will start by going over motivational background in p-adic cohomology theories, and then give a rough overview of main ideas and results in the paper "Prisms and prismatic cohomology" by Bhatt-Scholze. If time permits, we will also briefly discuss how the prismatic theory may reveal a deeper understanding of p-adic Galois representations.

Reference

1. "Prisms and prismatic cohomology" by Bhargav Bhatt and Peter Scholze, Annals of Mathematics

2. "Prismatic F-crystals and crystalline Galois representations" by Bhargav Bhatt and Peter Scholze

Syllabus

Lecturer Intro

Yong Suk Moon joined BIMSA in 2022 fall as an assistant research fellow. His research area is number theory and arithmetic geometry. More specifically, his current research focuses on p-adic Hodge theory, Fontaine-Mazur conjecture, and p-adic Langlands program. He completed his Ph.D at Harvard University in 2016, and was a Golomb visiting assistant professor at Purdue University (2016-19) and a postdoctoral researcher at University of Arizona (2019 - 22).

Lecturer Email: ysmoon1@gmail.com

TA: Dr. Zheng Xu, xuzheng1@mail.ustc.edu.cn