The 2-adic Eigencurve is Proper
Number Theory
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0503362,
title = {The 2-adic Eigencurve is Proper},
author = {Kevin Buzzard and Frank Calegari},
journal= {arXiv preprint arXiv:math/0503362},
year = {2007}
}