Abstract

In this paper we define Banach spaces of overconvergent half-integral weight p-adic modular forms and Banach modules of families of overconvergent half-integral weight p-adic modular forms over admissible open subsets of weight space. Both spaces are equipped with a continuous Hecke action for which U_p² is moreover compact. The modules of families of forms are used to construct an eigencurve parameterizing all finite-slope systems of eigenvalues of Hecke operators acting on these spaces. We also prove an analog of Coleman’s theorem stating that overconvergent eigenforms of suitably low slope are classical.

Keywords

modular forms of half-integral weight, p-adic modular forms, eigenvarieties

Mathematical Subject Classification

Primary: 11F33

Secondary: 14G22, 11F37

Authors

Appendix Authors