Kisin modules with descent data and parahoric local models

2015/10/26 by Ana Caraiani, Caraiani, Ana, Brandon Levin +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1510.07503

38 pages, final version, to appear in Ann. Sci. de l'ENS

arxiv created 2018/01/11 · arxiv updated 2018/01/15

Abstract

We construct a moduli space Y^{μ, τ} of Kisin modules with tame descent datum τ and with fixed 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/ℚp GL_n, cocharacter \ μ\, and parahoric level structure. We use this to construct the analogue of Kottwitz-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.

Related

• Phi-modules and coefficient spaces
• Local geometry of moduli stacks of two-dimensional Galois representations
• The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups
• Reductions of some two-dimensional crystalline representations via Kisin modules
• Connectedness of Kisin varieties for GL₂