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arXiv · 1701.05721

Irreducible components of the eigencurve of finite degree are finite over the weight space

Shin Hattori·James Newton
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Abstract

Let p be a rational prime and N a positive integer which is prime to p. Let W be the p-adic weight space for GL_{2,Q}. Let C_N be the p-adic Coleman-Mazur eigencurve of tame level N. In this paper, we prove that any irreducible component of C_N which is of finite degree over W is in fact finite over W. Combined with an argument of Chenevier and a conjecture of Coleman-Mazur-Buzzard-Kilford (which has been proven in special cases, and for general quaternionic eigencurves) this shows that the only finite degree components of the eigencurve are the ordinary components.

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Shin Hattori, James Newton. 2017-01-20. Irreducible components of the eigencurve of finite degree are finite over the weight space. https://arxiv.org/abs/1701.05721

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