2024/04/25 by Shun Ohkubo, Ohkubo, Shun
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.16291
openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a complete non-archimedean valuation field of characteristic 0, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over K, where decompositions regarding the extrinsic subsidiary ∂-generic radii of convergence in the sense of Kedlaya-Xiao. Our result is a refinement of a previous decomposition theorem due to Kedlaya and Xiao. As a key step in the proof, we prove a decomposition theorem in a stronger form in the case where K is equipped with a single derivation. To achieve this goal, we construct an object f0*L0 representing the usual dual functor and study some filtrations of f0*L0, which is used to construct the direct summands appearing in our decomposition theorem.