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arXiv · 2310.15732

Log prismatic Dieudonn\'e theory for log $p$-divisible groups over $\mathcal{O}_{K}$

Matti Würthen·Heer Zhao
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Abstract

Let $\mathcal{O}_{K}$ be a complete discrete valuation ring of mixed characteristic with perfect residue field, endowed with its canonical log-structure. We prove that log $p$-divisible groups over $\mathcal{O}_{K}$ correspond to Dieudonn\'e crystals on the absolute log-prismatic site of $\mathcal{O}_{K}$ endowed with the Kummer log-flat topology. The proof uses log-descent to reduce the problem to the classical prismatic correspondence, recently established by Ansch\"utz-Le Bras.

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Matti Würthen, Heer Zhao. 2023-10-24. Log prismatic Dieudonn\'e theory for log $p$-divisible groups over $\mathcal{O}_{K}$. https://arxiv.org/abs/2310.15732

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