A Note on Hodge-Tate Spectral Sequences

2022/06/20 by Zhiyou Wu, Wu, Zhiyou
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2206.09795

openalex publication_date 2022/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Hodge-Tate spectral sequence of a proper smooth rigid analytic variety can be reconstructed from its infinitesimal \mathbbB_dR⁺-cohomology through the Bialynicki-Birula map. A refinement of the decalage functor Lη is introduced to accomplish the proof. Further, we give a new proof of the torsion-freeness of the infinitesimal \mathbbB_dR⁺-cohomology independent of Conrad-Gabber spreading theorem, and a conceptual explanation that the degeneration of Hodge-Tate spectral sequences is equivalent to that of Hodge-de Rham spectral sequences.

Related

• The relative Hodge-Tate spectral sequence for rigid analytic spaces
• La suite spectrale de Hodge-Tate
• Spectral Rigidity and Algebraicity: A Unified Framework for the Hodge Conjecture
• Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds
• The relative Hodge-Tate spectral sequence -- an overview