Academy of Mathematics and Systems Science, CAS                         Colloquia & Seminars                                                   |                                                                                                                           | Speaker: |                                                 Prof. Shanwen Wang,Renmin University of China                          |                                                                  | Inviter: |                          |                                                                                          Title:                          |                         Completed cohomology              of modular curves and its factorization |                                                                                          Time & Venue:                          |                         2021.06.22 09:30-11:00              MCM110 & Zoom (Zoom ID: 4663562952 Password: mcm1234) |                                                                                          Abstract:                          |                                                 In this talk, we will explain a refinement of Emerton's factorization                of completed cohomology of modular curves, which is determined by                the factorization at the classical points. The main ingredient is                the q-expansion of the elements of the completed cohomology. This                is a part of the joint work with Pierre Colmez on the factorization                of Beilinson-Kato system.                          |                                                                   |                                                                           |                                                                |