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

• Luis Dieulefait ^[1] ; Adrián Zenteno ^[2]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  2. [2] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 2, 2020, págs. 635-655
• Idioma: inglés
• DOI: 10.2422/2036-2145.201609_016
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• Resumen

  • 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.