THE HALF-INTEGRAL WEIGHT EIGENCURVE by
نویسنده
چکیده
— In 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 Up2 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.
منابع مشابه
ar X iv : 0 90 6 . 32 49 v 1 [ m at h . N T ] 1 7 Ju n 20 09 THE HALF - INTEGRAL WEIGHT EIGENCURVE
— In 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 p2 is moreover compact. The modules of families of forms are used to construct an eigencurve ...
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