Local to Global Compatibility on the Eigencurve (l not equal p)

2007/09/26 by Alexander Paulin, Paulin, Alexander
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.0709.4190

arxiv created 2007/09/26 · arxiv updated 2009/12/01

Abstract

We generalise Coleman's construction of Hecke operators to define an action of GL₂(Q_l) on the space of finite slope overconvergent p-adic modular forms (l not equal p). In this way we associate to any C_p-valued point on the tame level N Coleman-Mazur eigencurve an admissible smooth representation of GL₂(Q_l) extending the classical construction. Using the Galois theoretic interpretation of the eigencurve we associate a 2-dimensional Weil-Deligne representation to such points and show that away from a discrete set they agree under the Local Langlands correspondence.

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