# Questions tagged [galois-representations]

Questions relating to the representations of the absolute Galois group $\mathrm{Gal}(\overline K/K)$ of a number field or of a local field.

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### How do we explicitly compute the Galois action on etale cohomology?

The general theorems about etale cohomology are usually enough to let us compute a given $\mathrm{H}^i(X,\mathbf{Q}_\ell)$ as a $\mathbf{Q}_\ell$-vector space without too much difficulty. I would like ...
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### Converse to Proposition 2.23 in Darmon, Diamond, Taylor's FLT Notes

Can someone either prove or link me to a reference for Remark 2.24 (page 64) here? I am told that SGA7 covers this for general abelian varieties. I am wondering if a) anyone can pinpoint where in SGA7 ...
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### Method of associating Galois representation to normalized Hecke eigenform of weight 2 not work for other weights. Why?

I have read some parts of "A first course in Modular forms" to understand the process of associating a Galois representation to modular forms. In the book it is done only for weight 2 but I ...
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### Commutative algebra details on patching when proving $R = \mathbb{T}$ theorem (Calegari-Geraghty Paper)

I've been working on understanding the proof of Fermat's last theorem and now focusing on the patching technique for modularity lifting. I found that the patching technique described in the paper ...
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### On ${\Bbb Z}/m{\Bbb Z}$-torsors.

I would like to know the explicit construction of ${\Bbb Z}/m{\Bbb Z}$-torsor $Y$'s over a scheme $X$. It is explained that $X$ are classified by $H_{et}^1(X, {\Bbb Z}/m{\Bbb Z})$, which is far from ...
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### some questions about the Robba ring

Notations and definitions Let $p$ be a prime integer, $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. Definition 1 We put  \mathcal{R}_r=\bigg\{ \sum_{i\in \...
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### How to define the Stiefel-Whitney class of a complex orthogonal representation?

Background: One of the main objects of interest in the theory of $L$-functions is the root number, a complex number of modulus one which appears in the functional equation. In general, a root number ...
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