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

2017/01/20 by Shin Hattori, Hattori, Shin, James Newton +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1701.05721

openalex publication_date 2017/01/20 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

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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