Kisin modules with descent data and parahoric local models

Ana Caraiani; Brandon Levin

doi:10.24033/asens.2354

Kisin modules with descent data and parahoric local models

Ana Caraiani
, Brandon Levin

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We construct a moduli space Y^μ,τ of Kisin modules with tame descent datum r and with p-adic Hodge type ≤ μ, for some finite extension K/ℚ_p. We show that this space is smoothly equivalent to the local model for Res_K/ℚ GL_n, cocharacter {μ}, and parahoric level structure. We use this to construct the analog of Kottwit'z-Rapoport strata on the special fiber Y^μ,τ indexed by the μ-admissible set. We also relate Y^μ,τ to potentially crystalline Galois deformation rings.

Original language	English (US)
Pages (from-to)	181-213
Number of pages	33
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	51
Issue number	1
DOIs	https://doi.org/10.24033/asens.2354
State	Published - Jan 1 2018
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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abstract = "We construct a moduli space Yμ,τ of Kisin modules with tame descent datum r and with p-adic Hodge type ≤ μ, for some finite extension K/ℚp. We show that this space is smoothly equivalent to the local model for ResK/ℚ GLn, cocharacter \{μ\}, and parahoric level structure. We use this to construct the analog of Kottwit'z-Rapoport strata on the special fiber Yμ,τ indexed by the μ-admissible set. We also relate Yμ,τ to potentially crystalline Galois deformation rings.",

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AU - Levin, Brandon

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AB - We construct a moduli space Yμ,τ of Kisin modules with tame descent datum r and with p-adic Hodge type ≤ μ, for some finite extension K/ℚp. We show that this space is smoothly equivalent to the local model for ResK/ℚ GLn, cocharacter {μ}, and parahoric level structure. We use this to construct the analog of Kottwit'z-Rapoport strata on the special fiber Yμ,τ indexed by the μ-admissible set. We also relate Yμ,τ to potentially crystalline Galois deformation rings.

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Kisin modules with descent data and parahoric local models

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