Workshop on Perfectoid Approach to P-adic Modular Forms

2021.08.03-08.05
Beijing, China

Date

Time

Speaker

Content

Aug 3

at

MCM

9:00-10:00

Yiwen Ding

Introduction of Pan’s paper: Give a gentle introduction on Pan’s paper, especially explaining how the previously discussed p-adic theories are related.

10:30-11:30

Hui Gao

Colmez–Tate–Sen Theory I: Give the standard Colmez–Tate–Sen axiom and quickly indicate the proof (following [BC08]); Discuss the case of fields and the case for decompletion process for overconvergent (？, Γ)-modules.

13:00-14:30

Liang Xiao

Colmez–Tate–Sen Theory II: Introduce basic concept of locally analytic vectors. Computation of locally analytic vectors in the case when the p-adic tower of extension contains the cyclotomic tower, following [BC16, §1-3]. Also include the results in [Pan, §2] (without the proof). If time permits, shortly discuss the generalization in [Be16, § 2].

14:45-15:45

Yiwen Ding

Locally analytic vectors in the geometric setup I: Cover [Pan, §3.1–3.3].

16:00-17:00

Liang Xiao

Locally analytic vectors in the geometric setup II: Cover [Pan, §3.4-3.6].

Aug 5

at

MCM

9:00-10:00

Liang Xiao

Computation of n-cohomology of locally analytic vectors I [Pan, §5.1-5.2].

10:30-11:30

Liang Xiao

Computation of n-cohomology of locally analytic vectors II [Pan, §5.3-5.4].

13:00-14:00

Yiwen Ding

Ext¹ conjecture of locally analytic representations: Introduce Breuil-Ding functor, and the functorial interpretation of Breuil’s Ext¹ conjecture.

14:30-15:30

Yiwen Ding

Ext¹ conjecture of locally analytic representations II: Introduce Breuil-Ding functor, and the functorial interpretation of Breuil’s Ext¹ conjecture.

15:30-17:00

Free discussion