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math/0503362

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Title: The 2-adic Eigencurve is Proper
Authors: Kevin Buzzard, Frank Calegari
Categories: math.NT Number Theory

Abstract: 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 the Eigencurve has no "holes"; given a punctured disc of finite slope overconvergent eigenforms over weight space, the center can be "filled in" with a finite slope overconvergent eigenform.

Owner: Frank Calegari
Version 1: Thu, 17 Mar 2005 16:16:19 GMT

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