Images of Galois representations in mod p Hecke algebras

@article{Amoros2017ImagesOG,
  title={Images of Galois representations in mod p Hecke algebras},
  author={Laia Amoros},
  journal={arXiv: Number Theory},
  year={2017}
}
  • L. Amoros
  • Published 21 February 2017
  • Mathematics
  • arXiv: Number Theory
Let $(\mathbb{T}_f,\mathfrak{m}_f)$ denote the mod $p$ local Hecke algebra attached to a normalised Hecke eigenform $f$, which is a commutative algebra over some finite field $\mathbb{F}_q$ of characteristic $p$ and with residue field $\mathbb{F}_q$. By a result of Carayol we know that, if the residual Galois representation $\overline{\rho}_f:G_\mathbb{Q}\rightarrow\mathrm{GL}_2(\mathbb{F}_q)$ is absolutely irreducible, then one can attach to this algebra a Galois representation $\rho_f:G_… 

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