A quotient of the Lubin-Tate tower II

Johansson, Christian; Ludwig, Judith; Hansen, David

doi:10.1007/s00208-020-02104-3

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A quotient of the Lubin-Tate tower II

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Ludwig, Judith
Max Planck Institute for Mathematics, Max Planck Society;

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Hansen, David
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00208-020-02104-3
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arXiv:1812.08203.pdf
(Preprint), 516KB

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Citation

Johansson, C., Ludwig, J., & Hansen, D. (in press). A quotient of the Lubin-Tate tower II. Mathematische Annalen, Published Online - Print pending. doi:10.1007/s00208-020-02104-3.

Cite as: http://hdl.handle.net/21.11116/0000-0007-7B75-C

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.