Moduli Spaces and Related Topics Seminar | On the cohomology of BG

Abstract

In this talk, if time permits, we will discuss:

(1) classify order p group schemes over Spec(char p alg closed field) using Dieudonne modules;

(2) a new way of understanding Dieudonne modules in terms of cohomology of BG (due to Mondal);

(3) an attempt of using BG to construct a counterexample that Deligne--Illusie asked for (work of Antieau--Bhatt--Mathew);

(4) why this attempt cannot succeed (joint work in progress with Kubrak--Mondal), and how this attempt can be made successful (due to Petrov).

About the speaker

I am currently an associate professor at the Morningside Center of Mathematics, Beijing, China. My research interest mainly rests in arithmetic geometry. Currently I am mainly working on p-adic Hodge theory and related problems in various p-adic cohomology theory and p-adic geometry. I am also interested in algebraic geometry with an infinity categorical flavor, finding/studying concrete interesting geometric examples. One particular such of my current focus is finite flat commutative group schemes and their classifying stacks.

个人主页：

http://www.mcm.ac.cn/people/members/202207/t20220727_710956.html