Eigenvarieties for non-cuspidal modular forms over PEL Shimura varieties for U(r, 1)

06.06.2023 13:15 - 14:45

Adel Betina (U Copenhagen)

We construct eigenvarieties for unitary groups U(r,1) parametrizing systems of eigenvalues of overconvergent and locally analytic p-adic automorphic forms including Eisenstein families. This is achieved by refining the method of Andreatta--Iovita--Pilloni for cuspidal automorphic forms. The main novelty is to define subsheaves of the p-adic automorphic sheaves of Andreatta--Iovita--Pilloni by imposing a condition on the sections  at the boundary of a toroidal compactification.

The purpose of this construction is the study of the exceptional zeros conjecture of Katz p-adic L-functions for CM fields via p-adicEisenstein congruences. This talk is based on a joint work with Ming-Lun Hsieh.


H. Grobner, A. Mellit


SR 12, 2. OG, OMP 1