DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 211-232

Kevin Buzzard and Frank Calegari

The 2-adic Eigencurve is Proper.

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.

2000 Mathematics Subject Classification: 11F11, 14G35

Keywords and Phrases: Modular Forms, Modular Curves

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