The 2-adic Eigencurve is Proper

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.

Cited by in corpus (6)

• Spectral expansions of overconvergent modular functions
• The Eigencurve is Proper
• Représentations galoisiennes automorphes et conséquences arithmétiques des conjectures de Langlands et Arthur
• The eigencurve is proper at integral weights
• Irreducible components of the eigencurve of finite degree are finite over the weight space
• A modular proof of the properness of the Coleman-Mazur eigencurve