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Let $k$ be an algebraically closed field of characteristic $p > 0$, $X$ a variety over $k$. We say $X$ lifts to characteristic zero, if there exists a local ring $R$ containing $\mathbb Z$ with ...

Let $R$ be a discrete valuation ring with fraction field $K$ of characteristic zero and residue field $k$ of characteristic $p>0$. Assume $k$ is algebraically closed. I want to produce examples of ...

Let $R$ be a complete DVR with residue field $k$ algebraically closed of characteristic $p$ and fraction field $K$ of characteristic zero. Let $C$ be a stable curve (in the sense of Mumford-Deligne) ...