The Eigencurve is Proper

The Eigencurve is Proper

by Hansheng Diao

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Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points correspond to all finite slope overconvergent p-adic eigenforms. We prove the conjecture that the eigencurve Cp,N is proper over the weight space for any prime p and tame level N.

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