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- Title
A note on Hodge–Tate spectral sequences.
- Authors
WU, ZHIYOU
- Abstract
We prove that the Hodge–Tate spectral sequence of a proper smooth rigid analytic variety can be reconstructed from its infinitesimal $\mathbb{B}_{\text{dR}}^+$ -cohomology through the Bialynicki–Birula map. We also give a new proof of the torsion-freeness of the infinitesimal $\mathbb{B}_{\text{dR}}^+$ -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.
- Subjects
EXPLANATION; INFINITESIMAL geometry
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2024, Vol 176, Issue 3, p625
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004124000069