Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties

2016/05/17 by Riccardo Brasca, Giovanni Rosso, Brasca, Riccardo +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1605.05065

Abstract

Generalising the recent method of Andreatta, Iovita, and Pilloni for cuspidal forms, we construct an eigenvariety for symplectic and unitary groups that parametrises systems of eigenvalues of overconvergent and locally analytic p-adic automorphic forms. This is achieved by gluing some intermediates eigenvarieties of a fixed 'degree of cuspidality'. The dimension of these eigenvarieties is explicit and depends on the degree of cuspidality, it is maximal for cuspidal forms and it is 1 for forms that are 'not cuspidal at all'. Under mild assumption, we are able to prove a conjecture of Urban about the dimension of the irreducible components of Hansen's eigenvariety in the case of the group GSp₄ over ℚ.

Cited by

• p-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus

Related

• Eigenvarieties for cuspforms over PEL type Shimura varieties with dense ordinary locus
• p-adic families of automorphic forms over some unitary Shimura varieties
• A derived construction of eigenvarieties
• Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
• P-Adic families of Siegel modular cuspforms