  Displays can be thought of as relative versions of Fontaine's notion of
strongly divisible lattice from integral $p$-adic Hodge theory. In favourable
circumstances, the crystalline cohomology of a smooth projective $R$-scheme $X$
is endowed with a display-structure coming from complexes associated with the
relative de Rham-Witt complex $W\Omega_{X/R}^{\bullet}$ of [LZ04]. In this
article, we use the crystal of relative displays of [GL21] to prove a
Grothendieck-Messing type result for the deformation theory of Calabi-Yau
threefolds.
