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 GSpin Shimura varieties. In such cases, the ordinary locus may be empty and we need to work with the μ-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.
