Abstract
The Hirokado variety is a Calabi–Yau threefold in characteristic 3 that is not liftable either to characteristic 0 or the ring W 2 of the second Witt vectors. Although Deligne–Illusie–Raynaud type Kodaira vanishing cannot be applied, we show that H 1(X, L −1) = 0, for an ample line bundle such that L 3 has a non-trivial global section, holds for this variety.
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