## STNB2017(31è any)

### Galois representations with values in mod p Hecke algebras

#### Ponents

Laia Amorós Carafí

#### Resum

I will explain how one can construct Galois representations that take values in local mod $p$ Hecke $\mathbb{F}_q$-algebras. I will then show how one can compute explicitly the image of such a Galois representation assuming that the corresponding residual representation has big image. Finally I will show some computations of these images in concrete examples.

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