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Deformations of Calabi--Yau varieties over transversal or crystalline prisms
Abstract
Recent work of Brantner and Taelman shows that derived deformation theory and period maps can recover strong mixed-characteristic lifting results. In this paper, we develop a prismatic version of this method for Calabi--Yau varieties over transversal or crystalline prisms, constructing compatible deformations over A/In for every n under suitable hypotheses. We also apply our method to F-split Calabi--Yau varieties over a field k of characteristic p>2. In particular, we consider an F-split smooth proper variety X of dimension d over an algebraically closed field k of characteristic p>2, with Hd−1(X,OX)=0 and trivial canonical bundle. We show that X admits a lift to W3(k).
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BibTeX
@misc{shi2026deformations,
title = {{Deformations of Calabi--Yau varieties over transversal or crystalline prisms}},
author = {Tingxiao Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41727},
eprint = {2610.41727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41727},
}
RIS
TY - UNPB
TI - Deformations of Calabi--Yau varieties over transversal or crystalline prisms
AU - Tingxiao Shi
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41727
UR - https://arxiv.org/abs/2610.41727
AB - Recent work of Brantner and Taelman shows that derived deformation theory and period maps can recover strong mixed-characteristic lifting results. In this paper, we develop a prismatic version of this method for Calabi--Yau varieties over transversal or crystalline prisms, constructing compatible deformations over A/I^n for every n under suitable hypotheses. We also apply our method to F-split Calabi--Yau varieties over a field k of characteristic p>2. In particular, we consider an F-split smooth proper variety X of dimension d over an algebraically closed field k of characteristic p>2, with H^d−1(X,O_X)=0 and trivial canonical bundle. We show that X admits a lift to W_3(k).
ER -