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We study deformations of Calabi-Yau varieties in characteristic p using techniques from derived algebraic geometry. We prove a mixed characteristic analogue of the Bogomolov-Tian-Todorov theorem (which states that Calabi-Yau varieties in characteristic 0 are unobstructed), and we show that ordinary Calabi-Yau varieties admit canonical lifts to characteristic 0, generalising the Serre-Tate theorem on ordinary abelian varieties.
Brantner et al. (Fri,) studied this question.
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