A quotient of the Lubin-Tate tower II
Abstract
In this article we construct the quotient M_1/P(K) of the infinite-level Lubin-Tate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form (n-1,1) as a perfectoid space, generalizing results of one of the authors (JL) to arbitrary n and K/Q_p 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 the mod p local Langlands correspondence. An appendix by David Hansen gives a local proof of perfectoidness of M_1/P(K) when n = 2, and shows that M_1/Q(K) is not perfectoid for maximal parabolics Q not conjugate to P.
Keywords
Cite
@article{arxiv.1812.08203,
title = {A quotient of the Lubin-Tate tower II},
author = {Christian Johansson and Judith Ludwig and David Hansen},
journal= {arXiv preprint arXiv:1812.08203},
year = {2020}
}
Comments
final version, accepted for publication in Mathematische Annalen