The geometric level-raising conjecture for the eigencurve
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.
Sources & referencesView supporting material
Primary source
Alexander G. M. Paulin, “Failure of the Local to Global Principle in the Eigencurve”, arXiv:1001.2051 (2010).
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