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A non-liftable Calabi-Yau threefold in characteristic 3. (English) Zbl 0969.14028

Summary: We show the existence of a Calabi-Yau threefold in characteristic 3 with its third Betti number zero. This example admits no lifting to characteristic zero and hence indicates that a theorem by Deligne that any \(K3\) surface in positive characteristic has a lifting to characteristic zero cannot be generalized straightforward to the case of Calabi-Yau threefolds.

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J30 \(3\)-folds
14G15 Finite ground fields in algebraic geometry
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