Work

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

Year: 2016

Type: preprint

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 $\mathrm{GSp}_4$ over $\mathbb{Q}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1605.05065

Authors: Brasca, Riccardo, Rosso, Giovanni

Institutions: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Diderot, Concordia University, University of Cambridge

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Fonds Wetenschappelijk Onderzoek

Awards: PERfectoids, Completed cohomology, LAnglands correspondence and TORsion in the cohomology, G8238292487

OpenAlex ID: W4214784253

Cites:

Cited by: 4

Related to: 10