The half-integral weight eigencurve

Appendix by Brian ConradIn this paper we define Banach spaces of overconvergent half-integral weight p-adic modular forms and Banach modules of families of overconvergent halfintegral weight p-adic modular forms over admissible open subsets of weight space.Both spaces are equipped with a continuous Hecke action for which U p 2 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.