Geodesic
The 2-adic eigencurve is proper
Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 211-232.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Coleman and Mazur ask whether the Eigencurve has any "holes". We answer their question in the negative for the $2$-adic Eigencurve of tame level one.
Classification : 11F33, 11F85
Keywords: modular forms, modular curves, $U$-operator, overconvergent modular form 
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Buzzard, Kevin; Calegari, Frank. The 2-adic eigencurve is proper. Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 211-232. http://geodesic.mathdoc.fr/item/DOCMA_2006__S5__a18/