Global liftings between inner forms of GSp(4)

• Verfasst von: Rösner, Mirko [VerfasserIn]
• Verfasst von: Weissauer, Rainer [VerfasserIn]
• Titel: Global liftings between inner forms of GSp(4)
• Verf.angabe: Mirko Rösner, Rainer Weissauer
• E-Jahr: 2024
• Jahr: October 2024
• Umfang: 60 S.
• Fussnoten: Online verfügbar: 17. Mai 2024, Artikelversion: 27. Mai 2024 ; Gesehen am 18.11.2024
• Titel Quelle: Enthalten in: Journal of number theory
• Ort Quelle: Orlando, Fla. : Elsevier, 1969
• Jahr Quelle: 2024
• Band/Heft Quelle: 263(2024) vom: Okt., Seite 79-138
• ISSN Quelle: 1096-1658
• DOI: doi:10.1016/j.jnt.2024.04.010
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Automorphic representations
• Sach-SW: Endoscopy
• Sach-SW: Inner forms
• Sach-SW: Symplectic groups
• Sach-SW: Trace formula
• K10plus-PPN: 1908874899

Abstract

For reductive groups G over a number field we discuss automorphic liftings of cohomological cuspidal irreducible automorphic representations π of G(A) to irreducible cohomological automorphic representations of H(A) for the quasi-split inner form H of G, and other inner forms as well. We show the existence of nontrivial weak global cohomological liftings in many cases, in particular for the case where G is anisotropic at the archimedean places. A priori, for these weak liftings we do not give a description of the precise nature of the corresponding local liftings at the ramified places, nor do we characterize the image of the lifting. For inner forms of the group H=GSp(4) however we address these finer questions. Especially, we prove the recent conjectures of Ibukiyama and Kitayama on paramodular newforms of square-free level.