Number Theory Seminar 28.06.2024

Speaker: Adel Betina (KU).

Title: Eigenvarieties for non-cuspidal automorphic forms over PEL Shimura varieties.

Abstract: We construct Eigenvarieties parametrizing locally analytic overconvergent  p-adic automorphic forms including Eisenstein families for unitary and symplectic groups. This is achieved by refining the method of Andreatta--Iovita--Pilloni for cuspidal automorphic forms and a deep study of the Hodge—Tate period map at the boundary of a toroidal compactification. The main novelty is the construction of subsheaves of the p-adic automorphic sheaves of Andreatta--Iovita--Pilloni by imposing a condition on the sections at the boundary. This talk is based on a joint work with Brasca—Rosso.