p-adic family of modular forms on GSpin Shimura varieties
Xiaoyu Zhang (Universität Duisburg-Essen)
Abstract: The theory of $p$-adic interpolation of modular forms on the upper half plane started with Serre for Eisenstein series and then was developed by Hida for ordinary cuspidal modular forms. This theory plays an important role in the construction of $p$-adic $L$-functions, modularity theorems, etc. In this talk, I will generalize this theory to modular forms on $\mathrm{GSpin}$ Shimura varieties. In such cases, the ordinary locus may be empty and we need to work with the $\mu$-ordinary locus. Then we follow Hida’s idea to construct $p$-adic families of modular forms and give the control theorem on the dimension of the space of such $p$-adic families.
algebraic geometrynumber theoryrepresentation theory
Audience: researchers in the topic
Comments: Zoom number: 682 6223 4350
Password: 300890
POINTS - Peking Online International Number Theory Seminar
Series comments: Description: Seminar on number theory and related topics
This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.
The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn
Organizers: | Marc Besson*, Yiwen Ding, Wen-Wei LI*, Ruochuan Liu, Zhiyu Tian, Liang Xiao, Enlin Yang, Xinyi Yuan |
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