# Dihedral universal deformations

@article{Deo2020DihedralUD,
title={Dihedral universal deformations},
author={Shaunak V. Deo and Gabor Wiese},
journal={Research in Number Theory},
year={2020},
volume={6},
pages={1-37}
}
• Published 14 May 2018
• Mathematics
• Research in Number Theory
This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic number theory, (3) modularity. As to (1), we prove that the universal deformation is dihedral if all infinitesimal deformations are dihedral. Concerning (2) in the setting of Galois representations of number fields, we give sufficient conditions to ensure…
1 Citations

### On the $\mu$ equals zero conjecture for the fine Selmer group in Iwasawa theory

• Mathematics
• 2022
. We study the Iwasawa theory of the ﬁne Selmer group associated to certain Galois representations. The vanishing of the µ -invariant is shown to follow in some cases from a natural property satisﬁed

## References

SHOWING 1-10 OF 58 REFERENCES

### Modularity lifting beyond the Taylor–Wiles method

• Mathematics
• 2012
We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been

### Classical and overconvergent modular forms

The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvea [G,

### NOTES ON THE ARITHMETIC OF HILBERT MODULAR FORMS

• Mathematics
• 2011
The purpose of this semi-expository article is to give another proof of a classical theorem of Shimura on the critical values of the standard L-function attached to a Hilbert modular form. Our proof

### Overconvergent modular forms and the Fontaine-Mazur conjecture

We prove a conjecture of Fontaine and Mazur on modularity of representations of Gℚ which are potentially semi-stable at p, for representations coming from finite slope, overconvergent eigenforms. We

### Twists of Hilbert modular forms

• Mathematics
• 1993
The theory of newforms for Hilbert modular forms is summarized including a statement of a strong multiplicity-one theorem and a characterization of newforms as eigenfunctions for a certain involution

### On the local behaviour of ordinary -adic representations

• Mathematics
• 2004
In this paper we study the local behaviour of the Galois representations attached to ordinary �-adic forms and ordinary classical cusp forms. In both cases the splitting of the local representation

### Class groups and local indecomposability for non-CM forms

• Mathematics
Journal of the European Mathematical Society
• 2021
Author(s): Castella, Francesc; Wang-Erickson, Carl; Hida, Haruzo | Abstract: In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those

### On abelian varieties with complex multiplication as factors of the abelian variety attached to Hilbert modular forms

In his papers [7] and [10], Hecke proved that every L-function with a Hecke character of an imaginary quadratic field is obtained as the Mellin transformation of a cusp form with respect to a certain

### The L-functions and modular forms database

• Mathematics, Computer Science
• 2021
The Langlands program, a set of conjectures relating objects from arithmetic algebraic geometry with modular and automorphic forms via Galois representations and Lfunctions, is the core of the LMFDB, a database of mathematical objects and the connections between them.