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  A quotient of the Lubin-Tate tower II

Johansson, C., Ludwig, J., & Hansen, D. (2021). A quotient of the Lubin-Tate tower II. Mathematische Annalen, 380(1-2), 43-89. doi:10.1007/s00208-020-02104-3.

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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 Creators:
Johansson, Christian, Author
Ludwig, Judith1, Author           
Hansen, David1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Number Theory
 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.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1812.08203
DOI: 10.1007/s00208-020-02104-3
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Title: Mathematische Annalen
  Abbreviation : Math. Ann.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 380 (1-2) Sequence Number: - Start / End Page: 43 - 89 Identifier: -