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For a cuspidal automorphic representation of GL2/Q associated to a modularform, the local and global Langlands correspondences are compatible at allfinite places of Q. On the p-adic Coleman-Mazur eigencurve this principle canfail (away from p) under one of two conditions: on a generically principalseries component where monodromy vanishes; or on a generically specialcomponent where the ratio of the Satake parameters degenerates. We prove, undermild restrictive hypotheses, that such points are the intersection ofgenerically principal series and special components. This is a geometricanalogue of Ribet's level raising and lowering theorems.

Failure of the Local to Global Principle in the Eigencurve