Eigenvarieties for cuspforms over PEL type Shimura varieties with dense ordinary locus

2014/07/30 by Riccardo Brasca, Brasca, Riccardo
Mathematics · #11F55 (Primary) 11F33 (Secondary #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33 #msc:11F55

paper · pdf · doi:10.48550/arxiv.1407.7973

28 pages, final version. To appear in Canadian Journal of Mathematics

arxiv created 2015/11/02 · arxiv updated 2015/11/03

Abstract

Let p>2 be a prime and let X be a compactified PEL Shimura variety of type (A) or (C) such that p is an unramified prime for the PEL datum. Using the geometric approach of Andreatta, Iovita, Pilloni, and Stevens we define the notion of families of overconvergent locally analytic p-adic modular forms of Iwahoric level for X. We show that the system of eigenvalues of any finite slope cuspidal eigenform of Iwahoric level can be deformed to a family of systems of eigenvalues living over an open subset of the weight space. To prove these results, we actually construct eigenvarieties of the expected dimension that parametrize systems of eigenvalues appearing in the space of families of cuspidal forms.

Related

• Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties
• p-adic families of automorphic forms over some unitary Shimura varieties
• p-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus
• P-Adic families of Siegel modular cuspforms
• Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C