No CrossRef data available.
Article contents
A note on Hodge–Tate spectral sequences
Published online by Cambridge University Press: 22 March 2024
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.
Keywords
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 3 , May 2024 , pp. 625 - 642
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Cambridge Philosophical Society