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

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

2007-09-26

arxiv.org/abs/0709.4190v1

Mathematics

Number Theory

Scientific paper

We generalise Coleman's construction of Hecke operators to define an action of GL_2(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 GL_2(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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