Siegel modular varieties and the Eisenstein cohomology of PGL2g+1

• Verfasst von: Weselmann, Uwe [VerfasserIn]
• Titel: Siegel modular varieties and the Eisenstein cohomology of PGL2g+1
• Verf.angabe: Uwe Weselmann
• E-Jahr: 2014
• Jahr: 13 May 2014
• Umfang: 46 S.
• Teil: volume:145
• Teil: year:2014
• Teil: number:1
• Teil: pages:175-220
• Teil: extent:46
• Fussnoten: Im Titel sind "2g+1" tiefgestellt ; Gesehen am 27.09.2021
• Titel Quelle: Enthalten in: Manuscripta mathematica
• Ort Quelle: Berlin : Springer, 1969
• Jahr Quelle: 2014
• Band/Heft Quelle: 145(2014), 1, Seite 175-220
• ISSN Quelle: 1432-1785
• DOI: doi:10.1007/s00229-014-0676-8
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 177191064X

Abstract

We use the twisted topological trace formula developed in Weselmann (Compos. Math. 148:65-120, 2012) to understand liftings from symplectic to general linear groups. We analyse the lift from SP2gto PGL2g+1 over the ground field $${\mathbb{Q}}$$in further detail, and we get a description of the image of this lift of the L2 cohomology of SP2g(which is related to the intersection cohomology of the Shimura variety attached to GSp2g) in terms of the Eisenstein cohomology of the general linear group, whose building constituents are cuspidal representations of Levi groups. This description may be used to understand endoscopic and CAP-representations of the symplectic group.