Stable infinity-categories with left and right complete t-structures have deformation functors that are formal E2-moduli problems determined by their Hochschild cohomology.
Deformations and Lifts of Calabi-Yau Varieties in Characteristic $p$
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abstract
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.
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Hochschild cohomology and deformation theory of stable infinity-categories with t-structures
Stable infinity-categories with left and right complete t-structures have deformation functors that are formal E2-moduli problems determined by their Hochschild cohomology.