Fontaine-Laffaille Theory over Power Series Rings

2024/07/31 by Christian Hokaj, Hokaj, Christian
Mathematics · #11F80 (Primary) 11F85 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2407.21327

openalex publication_date 2024/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field of characteristic p > 2. We extend the equivalence of categories between Fontaine-Laffaille modules and ℤ_p lattices inside crystalline representations with Hodge-Tate weights at most p-2 of Fontaine and Laffaille to the situation where the base ring is the power series ring over the Witt vectors W(k)[ [ t₁, ⋯ , t_d] ] and where the base ring is a p-adically complete ring that is étale over the Tate Algebra W(k)⟨ t₁^{± 1}, ⋯ , t_d^{± 1}⟩.

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