A Note on Hodge-Tate Spectral Sequences

Zhiyou Wu

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arXiv · 2206.09795

A Note on Hodge-Tate Spectral Sequences

Zhiyou Wu

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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. A refinement of the decalage functor $L\eta$ is introduced to accomplish the proof. Further, we 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.

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Zhiyou Wu. 2022-06-20. A Note on Hodge-Tate Spectral Sequences. https://arxiv.org/abs/2206.09795

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