Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case-Reference-Cited by-同舟云学术

Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case

Published:2021-01-09 Issue: Volume: Page:
ISSN:0025-5831
Container-title:Mathematische Annalen
language:en
Short-container-title:Math. Ann.

Author:

Imai Naoki^ORCID,Tsushima Takahiro

Abstract

AbstractWe construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet–Langlands correspondence for the simple supercuspidal representations. The reductions of the formal models are isomorphic to the perfections of some Artin–Schreier varieties, whose cohomology realizes primitive Galois representations. We show also the Tate conjecture for Artin–Schreier varieties associated to quadratic forms.

Funder

Japan Society for the Promotion of Science

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s00208-020-02106-1.pdf

Reference27 articles.

1. Bushnell, C.J., Henniart, G.: The essentially tame local Langlands correspondence, I. J. Am. Math. Soc. 18(3), 685–710 (2005)

2. Bushnell, C.J., Henniart, G.: Langlands parameters for epipelagic representations of $${\rm GL}_n$$. Math. Ann. 358(1–2), 433–463 (2014)

3. Bushnell, C.J., Henniart, G.M., Kutzko, P.C.: Local Rankin-Selberg convolutions for $${\rm GL}_n$$: explicit conductor formula. J. Am. Math. Soc. 11(3), 703–730 (1998)

4. Boyer, P.: Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale. Invent. Math. 138(3), 573–629 (1999)

5. Boyarchenko, M., Weinstein, J.: Maximal varieties and the local Langlands correspondence for $$GL(n)$$. J. Am. Math. Soc. 29(1), 177–236 (2016)

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