Endoscopy on SL2-eigenvarieties

• Verfasst von: Johansson, Christian [VerfasserIn]
• Verfasst von: Ludwig, Judith [VerfasserIn]
• Titel: Endoscopy on SL2-eigenvarieties
• Verf.angabe: by Christian Johansson at Gothenburg and Judith Ludwig at Heidelberg
• E-Jahr: 2024
• Jahr: 28. Mai 2024
• Umfang: 79 S.
• Fussnoten: Gesehen am 03.09.2024
• Titel Quelle: Enthalten in: Journal für die reine und angewandte Mathematik
• Ort Quelle: Berlin : de Gruyter, 1826
• Jahr Quelle: 2024
• Band/Heft Quelle: (2024), 813, Seite 1-79
• ISSN Quelle: 1435-5345
• DOI: doi:10.1515/crelle-2024-0026
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1901025292

Abstract

In this paper, we study ????-adic endoscopy on eigenvarieties for SL 2 \mathrm{SL}_{2} over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic ????-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the SL 2 \mathrm{SL}_{2} -eigenvariety is locally a quotient of an eigenvariety for GL 2 \mathrm{GL}_{2} , which allows us to explicitly describe the local geometry of the SL 2 \mathrm{SL}_{2} -eigenvariety. In particular, we show that it often fails to be Gorenstein.