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Let $\mathcal{O}_{K}$ be a complete discrete valuation ring of mixedcharacteristic with perfect residue field, endowed with its canonicallog-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 useslog-descent to reduce the problem to the classical prismatic correspondence,recently established by Ansch\"utz-Le Bras.

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