# 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_… ## Tables from this paper ## References SHOWING 1-10 OF 17 REFERENCES Deforming Galois Representations Given a continuous homomorphism $${G_{Q,S}}G{L_2}\left( {{Z_p}} \right)$$ where Gℚ,S is the Galois group of the maximal algebraic extension of ℚ unramified outside the finite set S of primes of A structure theorem for subgroups of GLn over complete local Noetherian rings with large residual image Given a complete local Noetherian ring (A, mA) with finite residue field and a subfield k of A/mA, we show that every closed subgroup G of GLn(A) such that G mod mA ⊇ SLn(k) contains a conjugate of Structure of Hecke algebras of modular forms modulo p Generalizing the recent results of Bellaiche and Khare for the level 1 case, we study the structure of the local components of the shallow Hecke algebras (i.e. Hecke algebras without Up and U` for REPRESENTATION THEORY FOR FINITE GROUPS We cover some of the foundational results of representation theory including Maschke’s Theorem, Schur’s Lemma, and the Schur Orthogonality Relations. We consider character theory, constructions of Commutative Ring Theory • Mathematics • 1989 Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7. Images of Galois representations and p-adic models of Shimura curves ADVERTIMENT. La consulta d’aquesta tesi queda condicionada a l’acceptació de les següents condicions d'ús: La difusió d’aquesta tesi per mitjà del servei TDX (www.tdx.cat) i a través del Dipòsit Commutative Algebra I 1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed Formes modulaires de poids$1\$
• Mathematics
• 1974
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