Irreducibility of automorphic Galois representations of GL(n), n at most 5

Calegari, Frank; Gee, Toby

doi:10.5802/aif.2817

Cited by 32 publications

(41 citation statements)

References 14 publications

(29 reference statements)

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“…Remark 3.4. As the results of [BLGGT14] and [CG13] (see also [CG17]) only works for a set of density one of primes, we are not able to prove in general that π is non exceptional for all but finitely many primes λ. However partial results are well known.…”

Section: -Reducible Imagesmentioning

confidence: 73%

On the images of the Galois representations attached to generic automorphic representations of GSp(4)

Dieulefait¹,

Zenteno²

2020

Annali Scuola Normale Superiore - Classe Di Scienze

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By making use of Langlands functoriality between GSp(4) and GL(4), we show that the images of the Galois representations attached to "genuine" globally generic automorphic representations of GSp(4) are "large" for a set of primes of density one. Moreover, by using the notion of (n, p)-groups (introduced by Khare, Larsen and Savin) and generic Langlands functoriality from SO(5) to GL(4) we construct automorphic representations of GSp(4) such that the compatible system attached to them has large image for all primes.

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Section: -Reducible Imagesmentioning

confidence: 73%

On the images of the Galois representations attached to generic automorphic representations of GSp(4)

Dieulefait¹,

Zenteno²

2020

Annali Scuola Normale Superiore - Classe Di Scienze

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“…Since F has a cohomological weight, by [68], π F,p is weakly equivalent to a generic cuspidal representation π = ⊗ ′ p π p of GSp 4 (A) so that {π F,∞ , π ∞ } makes up a L-packet of Π(GSp 4 (R)). Since F is non-endoscopic, the ℓ-adic Galois representation associated to F is irreducible by Chebotarev density theorem and [12].…”

Section: Proof Of the Main Theoremmentioning

confidence: 99%

An Equidistribution Theorem for Holomorphic Siegel Modular Forms for and Its Applications

Kim

Wakatsuki

Yamauchi³

2018

J. Inst. Math. Jussieu

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We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for GSp4/Q in various aspects. A main tool is Arthur's invariant trace formula. While Shin [58] and Shin-Templier [59] used Euler-Poincaré functions at infinity in the formula, we use a pseudocoefficient of a holomorphic discrete series to extract holomorphic Siegel cusp forms. Then the non-semisimple contributions arise from the geometric side, and this provides new second main terms A, B1 in Theorem 1.1 which have not been studied and a mysterious second term B2 also appears in the second main term coming from the semisimple elements. Furthermore our explicit study enables us to treat more general aspects in the weight. We also give several applications including the vertical Sato-Tate theorem, the unboundedness of Hecke fields and low-lying zeros for degree 4 spinor L-functions and degree 5 standard L-functions of holomorphic Siegel cusp forms. Spectral decomposition 204.2. Special cohomological representation of GSp 4 (R) 22

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“…On notera r j,k,ℓ la représentation ℓ-adique r f associée à cette forme f et à ℓ par le théorème ci-dessus. C'est une représentation irréductible d'après un résultat de Calegari et Gee [1] et le §X.1.3 de [3].…”

Section: Introductionunclassified

Images de représentations galoisiennes associées à certaines formes modulaires de Siegel de genre 2

Tayou

2017

Int. J. Number Theory

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Abstract. We study the image of the ℓ-adic Galois representations associated to the four vector valued Siegel modular forms appearing in the work of Chenevier and Lannes [3]. These representations are symplectic of dimension 4. Following methods used by Dieulefait in [4], we determine the primes ℓ for which these representations are absolutely irreducible. In addition, we show that their image is "full" for all primes ℓ such that the associated residual representation is absolutely irreducible, except in two cases.

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Irreducibility of automorphic Galois representations of GL(n), n at most 5

Cited by 32 publications

References 14 publications

On the images of the Galois representations attached to generic automorphic representations of GSp(4)

On the images of the Galois representations attached to generic automorphic representations of GSp(4)

An Equidistribution Theorem for Holomorphic Siegel Modular Forms for and Its Applications

Images de représentations galoisiennes associées à certaines formes modulaires de Siegel de genre 2

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