题目：A log p-divisible group has semi-stable reduction if and only if it extends to a log p-divisible group
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摘要：Let $R$ be a discrete valuation ring with field of fractions $K$, and let $p$ be the characteristic of the residue field of $R$. De Jong introduced the notion of having semi-stable reduction for $p$-divisible groups over $K$. In early 90's, Kazuya Kato developed a theory of log $p$-divisible groups, which serve as the degeneration of classical $p$-divisible groups and are expected to behave in the same way as the classical $p$-divisible group in the log sense. It is a general philosophy that the objects with semi-stable reduction correspond to non-degenerate objects in log geometry. We show that a log $p$-divisible group over $K$ has semi-stable reduction if and only if it extends to a log $p$-divisible group over $S=\SpecR$ (endowed with the canonical log structure). If time allows, we will state a few more results about log $p$-divisible groups, in order to justify the feature of log $p$-divisible groups mentioned above. This is based on a joint work with Alessandra Bertapelle.