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 ${\mathrm{GL}}_{2,\mathbb{Q}}$. 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 $𝒲$.

中文翻译：

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有限度本征曲线的不可约成分在权空间上是有限的

令p为有理素数，N为对p素数的正整数。让$𝒲$是...的p -adic权重空间${\mathrm{GL}}_{2，\mathbb{Q}}$。让${𝒞}_{ñ}$ 是驯服度N的p -adic Coleman-Mazur本征曲线。在本文中，我们证明了任何不可约成分${𝒞}_{ñ}$ 在一定程度上 $𝒲$ 实际上是有限的 $𝒲$。