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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 $X$ be a quasi-hyperelliptic surface in characteristic 3 where the canonical bundle $K_X$ is trivial. Question: Is there a finite étale covering $Y \rightarrow X$ such that $Y$ is an abelian ...