Constructing Hilbert modular forms without exceptional primes

Dieulefait, Luis; Zenteno, Adrián

doi:10.1007/s00209-017-1885-0

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2020

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“…In the same direction, stronger results have been proved in [DW11] and [DZ18] for compatible systems attached to classical and Hilbert modular forms. More precisely, in loc.…”

Section: Introductionmentioning

confidence: 84%

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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“…In the same direction, stronger results have been proved in [DW11] and [DZ18] for compatible systems attached to classical and Hilbert modular forms. More precisely, in loc.…”

Section: Introductionmentioning

confidence: 84%