All Questions
Tagged with hecke-algebras galois-representations
7 questions
3
votes
0
answers
156
views
Taylor-Wiles systems for higher dimensional deformation rings
Let $R$ be a deformation ring and $M$ be a finitely generated $R$-module.
A strategy for proving the theorems $R=T$ is to associate with $(R,M)$ a Taylor-Wiles system denoted $(R_{Q},M_{Q})$. Here I'm ...
- 1,270
3
votes
0
answers
102
views
List of techniques that have been used to prove topological properties of locus in the deformation ring or the Hecke algebra
My question is maybe going to be a bit vague. My apologies if so.
The setting:
Let $\overline{\rho}$ be a residual representation and $R$ be a deformation ring of $\overline{\rho}$.
Let $\mathbb{T}$ ...
- 1,270
2
votes
1
answer
172
views
Krull dimension of Hecke algebra (level 1) for p = 2, 3
Let $p$ be a prime and consider the ($p$-deprived) Hecke algebra $\mathbb{T}$ which the projective limit of the Hecke $\mathbb{Z}_p$-algebras $\mathbb{T}_k$ which act on modular forms of level $1$ ...
- 597
8
votes
1
answer
963
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Deligne-Scholl's motives for modular forms: Hecke operators vs. transposed Hecke operators
EDIT: I moved my original question down to the bottom. The question here at the top is related, at least I suppose that the same phenomenon is behind both of them.
In the article "Valeurs de ...
- 734
5
votes
1
answer
380
views
Smoothness of Hecke algebras
First I will introduce some notation and definitions.
Fix a level $N$ (take $N=1$ if it makes things easier) and a prime $p$. Let $k$ be a finite field of characteristic $p$ and let $\mathcal{C}$ be ...
- 597
2
votes
1
answer
491
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Newform and Galois representation (Shimura-Deligne Reciprocity Law)
Shimura-Deligne Reciprocity Law implies that to a newform $f \colon =f(z) \in S^{\mathrm{new}}_k(\Gamma_0(N))$ of weight $k$, one can associate Galois representation $\rho_{f,\lambda} \colon {\mathrm{...
- 101
3
votes
0
answers
519
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local deformation rings and Hecke algebras
Let $\bar{\rho}_p$ be a two-dimensional irreducible local Galois representation of $Gal(\bar{\mathbb{Q}}_p / \mathbb{Q}_p)$ on a $k$-vector space, where $k$ is a finite extension of $\mathbb{F}_p$. ...
