A quotient of the Lubin-Tate tower II
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 s...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Mathematische Annalen
Year: 2020, Volume: 380, Issue: 1, Pages: 43-89 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-020-02104-3 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00208-020-02104-3 Verlag, lizenzpflichtig, Volltext: https://link.springer.com/article/10.1007%2Fs00208-020-02104-3 
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| Author Notes: | Christian Johansson, Judith Ludwig, David Hansen |
| Summary: | 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. |
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| Item Description: | Published online: 9 November 2020 Gesehen am 01.06.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-020-02104-3 |