Local to Global Compatibility on the Eigencurve (l not equal p)
Number Theory
2007-09-27 v1
Abstract
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.
Cite
@article{arxiv.0709.4190,
title = {Local to Global Compatibility on the Eigencurve (l not equal p)},
author = {Alexander Paulin},
journal= {arXiv preprint arXiv:0709.4190},
year = {2007}
}