Construction of automorphic Galois representations, II

Chenevier, Gaëtan; Harris, Michael

doi:10.4310/cjm.2013.v1.n1.a2

Cited by 98 publications

(94 citation statements)

References 12 publications

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“…In the presence of such a self-duality assumption ('polarizability', see [9]) the existence of r p,ı (π) has been known for some years (see [18,51]). In almost all polarizable cases r p,ı (π) is realized in the cohomology of a Shimura variety, and in all polarizable cases r p,ı (π) ⊗2 is realized in the cohomology of a Shimura variety (see [16]).…”

Section: ∼ → C Suppose That E Is a Cm (Or Totally Real) Field And Thmentioning

confidence: 99%

“…(Alternatively it is presumably possible to construct an eigenvariety in this setting, but we have not carried this out.) One can attach Galois representations to these classical cusp forms by using the trace formula to lift them to polarizable, regular algebraic, discrete automorphic representations of GL 2n (A F ) (see, e.g., [52]) and then applying the results of Chenevier and Harris [18], Shin [51]. We learnt the idea that one might try to realize Π (N ) in a space of overconvergent p-adic cusp forms for G n (of finite slope) from Chris Skinner.…”

Section: ∼ → C Suppose That E Is a Cm (Or Totally Real) Field And Thmentioning

confidence: 99%

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On the rigid cohomology of certain Shimura varieties

Harris

Lan

Taylor³

et al. 2016

Res Math Sci

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171

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We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of GL n over a CM (or totally real) field and check local-global compatibility for the l-adic representation away from l and a finite number of rational primes above which the CM field or the automorphic representation ramifies. The main innovation is that we impose no self-duality hypothesis on the automorphic representation.

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Section: ∼ → C Suppose That E Is a Cm (Or Totally Real) Field And Thmentioning

confidence: 99%

Section: ∼ → C Suppose That E Is a Cm (Or Totally Real) Field And Thmentioning

confidence: 99%

On the rigid cohomology of certain Shimura varieties

Harris

Lan

Taylor³

et al. 2016

Res Math Sci

Self Cite

171

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“…On fixe un plongement Q −→ Q ℓ , ce qui nous fournit un morphisme de groupes Gal(Q ℓ /Q ℓ ) → Gal(Q/Q). D'après les rappels ci-dessus concernant la définition de r j,k,ℓ , et d'après [2], la représentation r j,k,ℓ est une Q ℓ -représentation cristalline de dimension 4, de poids de Hodge-Tate 0, k − 2, j + k − 1, et j + 2k − 3. Le théorème de Fontaine-Laffaille [5] admet donc la conséquence suivante.…”

Section: Action De L'inertieunclassified

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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“…We combine this theorem with the existence of Galois representation ( [23], [45], [37], [57], [21]; the precise statement we need is stated as [10, Theorems 1.1, 1.2]).…”

Section: Galois Representations V1 Recollectionsmentioning

confidence: 99%

On torsion in the cohomology of locally symmetric varieties

Scholze

2015

Ann. Math.

132

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Abstract. The main result of this paper is the existence of Galois representations associated with the mod p (or mod p m ) cohomology of the locally symmetric spaces for GL n over a totally real or CM field, proving conjectures of Ash and others. Following an old suggestion of Clozel, recently realized by Harris-Lan-Taylor-Thorne for characteristic 0 cohomology classes, one realizes the cohomology of the locally symmetric spaces for GL n as a boundary contribution of the cohomology of symplectic or unitary Shimura varieties, so that the key problem is to understand torsion in the cohomology of Shimura varieties.Thus, we prove new results on the p-adic geometry of Shimura varieties (of Hodge type). Namely, the Shimura varieties become perfectoid when passing to the inverse limit over all levels at p, and a new period map towards the flag variety exists on them, called the Hodge-Tate period map. It is roughly analogous to the embedding of the hermitian symmetric domain (which is roughly the inverse limit over all levels of the complex points of the Shimura variety) into its compact dual. The Hodge-Tate period map has several favorable properties, the most important being that it commutes with the Hecke operators away from p (for the trivial action of these Hecke operators on the flag variety), and that automorphic vector bundles come via pullback from the flag variety.

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Construction of automorphic Galois representations, II

Cited by 98 publications

References 12 publications

On the rigid cohomology of certain Shimura varieties

On the rigid cohomology of certain Shimura varieties

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

On torsion in the cohomology of locally symmetric varieties

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