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arXiv · 2311.07024

Hodge--Tate prismatic crystals and Sen theory

Hui Gao·Yu Min·Yupeng Wang
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Abstract

We study Hodge-Tate crystals on the absolute (log-) prismatic site of $\mathcal{O}_K$, where $\mathcal{O}_K$ is a mixed characteristic complete discrete valuation ring with perfect residue field. We first classify Hodge-Tate crystals by $\mathcal{O}_K$-modules equipped with certain small endomorphisms. We then construct Sen theory over a non-Galois Kummer tower, and use it to classify rational Hodge-Tate crystals by (log-) nearly Hodge-Tate representations. Various cohomology comparison and vanishing results are proved along the way.

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Hui Gao, Yu Min, Yupeng Wang. 2023-11-13. Hodge--Tate prismatic crystals and Sen theory. https://arxiv.org/abs/2311.07024

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