On properness of the eigencurve
Hansheng Diao, Ruochuan Liu
TL;DR
This paper proves that the Coleman-Mazur eigencurve exhibits properness over the weight space at many points, enhancing understanding of its geometric structure in number theory.
Contribution
It establishes the properness of the eigencurve at a broad class of points, a significant advancement in the study of p-adic families of modular forms.
Findings
Proves properness of the eigencurve at many points
Enhances understanding of eigencurve's geometric properties
Supports further research in p-adic modular forms
Abstract
We prove that the Coleman-Mazur eigencurve is proper (over the weight space) at a large class of points.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations