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2012 | OriginalPaper | Chapter

14. Deformations of Hyperbolic Structures and p-Adic Ordinary Modular Forms

Author : Masanori Morishita

Published in: Knots and Primes

Publisher: Springer London

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Abstract

In this final chapter, as an extension of the analogies in Chap. 13 to 2-dimensional representations, we discuss intriguing analogies between the family of holonomy representations associated to deformations of hyperbolic structures (due to W. Thurston) and the family of Galois representations associated to deformations of p-adic ordinary modular forms (due to H. Hida and B. Mazur).

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Footnotes
1
The analogy between two deformation spaces \(\mathcal{X}_{K}^{\circ}(\rho_{h})\) and \(\mathcal{X}_{p}^{\mathrm{H}}(\bar{\rho})\) was firstly pointed out by K. Fujiwara [Fw]. See also [Oh].
 
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Metadata
Title
Deformations of Hyperbolic Structures and p-Adic Ordinary Modular Forms
Author
Masanori Morishita
Copyright Year
2012
Publisher
Springer London
DOI
https://doi.org/10.1007/978-1-4471-2158-9_14

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