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arXiv · 2302.09882

Crystals of relative displays and Calabi-Yau threefolds

Oliver Gregory
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Abstract

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.

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Oliver Gregory. 2023-02-20. Crystals of relative displays and Calabi-Yau threefolds. https://arxiv.org/abs/2302.09882

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