The half-integral weight eigencurve

Details The half-integral weight eigencurve The half-integral weight eigencurve

2009-06-17

arxiv.org/abs/0906.3249v1

Algebra and Number Theory 2 (2008), no. 7, p. 755-808

Mathematics

Number Theory

Scientific paper

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 $U_{p^2}$ 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.

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