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A note on Hodge–Tate spectral sequences

Part of: Arithmetic problems. Diophantine geometry (Co)homology theory

Published online by Cambridge University Press:  22 March 2024

ZHIYOU WU
ZHIYOU WU*
Affiliation:
Morningside center of Mathematics, Chinese Academy of Sciences, No. 55, Zhongguancun East Road, Haidian District, Beijing 100190. e-mail: wuzhiyou@amss.ac.cn
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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

14G45

MSC classification

Secondary: 14F40: de Rham cohomology 14G22: Rigid analytic geometry
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

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