Venue: Lecture Hall of IASM, ZJU

Time: 16:00-17:00, December 25

Speaker: 江元旸 Yuanyang Jiang (Université Paris-Saclay)

Abstract: We generalize a result of Lue Pan on locally analytic completed cohomology of modular curves to the case of Hilbert modular varieties. As an application, we prove that for parallel weight Hecke classes appearing in the completed cohomology of Hilbert modular varieties, de Rhamness of the associated Galois representation will imply classicality. One central problem is to understand certain partial de Rham cohomology, which we will prove to be classical by developing a version of Jacquet–Langlands transfer of D-modules using theory of analytic de Rham stacks.