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math.NT2005★ 14 cited
The 2-adic Eigencurve is Proper
Kevin Buzzard, Frank Calegari
For p=2 and tame level N=1 we prove that the map from the (Coleman-Mazur) Eigencurve to weight space satisfies the valuative criterion of properness. More informally, we show that…
math.NT2005
Elliptic Curves of Odd Modular Degree
Frank Calegari, Matthew Emerton
The modular degree m_E of an elliptic curve E/Q is the minimal degree of any surjective morphism X_0(N) -> E, where N is the conductor of E. We give a necessarily set of criteria f…