The geometric level-raising conjecture for the eigencurve
Let be the cuspidal eigencurve associated with a modular two-dimensional residual representation, and let be the Weil–Deligne representation attached to . A component is generically principal series or generically special at according to the corresponding generic local representation type.
Geometric level-raising conjecture. If is a generically principal-series at component and there exists such that is one dimensional, then there exists a generically special irreducible component such that .
This is presented as a geometric analogue of Ribet's level-raising theorem and, together with the preceding statement, as equivalent to the main eigencurve intersection conjecture. The supplied text gives no resolution.
References
Primary source
Alexander G. M. Paulin, “Failure of the Local to Global Principle in the Eigencurve”, arXiv:1001.2051 (2010).
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