A quotient of the Lubin-Tate tower II

• Verfasst von: Johansson, Christian [VerfasserIn]
• Verfasst von: Ludwig, Judith [VerfasserIn]
• Verfasst von: Hansen, David [VerfasserIn]
• Titel: A quotient of the Lubin-Tate tower II
• Verf.angabe: Christian Johansson, Judith Ludwig, David Hansen
• Jahr: 2021
• Jahr des Originals: 2020
• Umfang: 47 S.
• Teil: volume:380
• Teil: year:2021
• Teil: number:1
• Teil: pages:43-89
• Teil: extent:47
• Fussnoten: Published online: 9 November 2020 ; Gesehen am 01.06.2021
• Titel Quelle: Enthalten in: Mathematische Annalen
• Ort Quelle: Berlin : Springer, 1869
• Jahr Quelle: 2021
• Band/Heft Quelle: 380(2021), 1, Seite 43-89
• ISSN Quelle: 1432-1807
• DOI: doi:10.1007/s00208-020-02104-3
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1759340790

Abstract

In this article we construct the quotient M1/P(K) of the infinite-level Lubin–Tate spaceM1 by the parabolic subgroup P(K) ⊂ GLn(K) of block form (n − 1, 1) as a perfectoid space, generalizing the results of Ludwig (Forum Math Sigma 5:e17, 41, 2017) to arbitrary n and K/Qp finite. For this we prove some perfectoidness results for certain Harris–Taylor Shimura varieties at infinite level. As an application of the quotient construction we show a vanishing theorem for Scholze’s candidate for the mod p Jacquet–Langlands and mod p local Langlands correspondence. An appendix by David Hansen gives a local proof of perfectoidness of M1/P(K) when n = 2, and shows thatM1/Q(K) is not perfectoid for maximal parabolics Q not conjugate to P.