All Strict Calabi--Yau Threefolds of Height One Lift to Characteristic 0
Abstract
We prove that every strict Calabi--Yau threefold of Artin--Mazur height one over an algebraically closed field k of characteristic p>0 admits a projective lift to W(k). No assumption is made on the torsion in its crystalline cohomology, and p is arbitrary. Using the crystalline period map of Brantner and Taelman, we show that the obstruction to extending a lift over W_n(k) is the Bockstein of a torsion coordinate of its period point, and that this coordinate can always be made to vanish by varying the lift. The mixed-characteristic deformation functor need not be smooth: for a Calabi--Yau threefold of height one constructed by Addington and Bragg in characteristic 3, some lifts over W_2(k) do not extend over W_3(k). This disproves a conjecture of Achinger and Zdanowicz.
Related
- The Tate Conjecture for Ordinary Calabi-Yau Threefolds
- Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds
- Degeneration of Calabi-Yau threefolds with Galois action induced by modular form of weight 3
- Stability conditions on Calabi-Yau threefolds of type K
- Rigid and obstructed tangent bundles on Calabi--Yau threefolds
BibTeX
@misc{ward2026strict,
title = {{All Strict Calabi--Yau Threefolds of Height One Lift to Characteristic 0}},
author = {Matthew Ward},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37075},
eprint = {2610.37075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37075},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All Strict Calabi--Yau Threefolds of Height One Lift to Characteristic 0
AU - Matthew Ward
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37075
UR - https://arxiv.org/abs/2610.37075
AB - We prove that every strict Calabi--Yau threefold of Artin--Mazur height one over an algebraically closed field k of characteristic p>0 admits a projective lift to W(k). No assumption is made on the torsion in its crystalline cohomology, and p is arbitrary. Using the crystalline period map of Brantner and Taelman, we show that the obstruction to extending a lift over W_n(k) is the Bockstein of a torsion coordinate of its period point, and that this coordinate can always be made to vanish by varying the lift. The mixed-characteristic deformation functor need not be smooth: for a Calabi--Yau threefold of height one constructed by Addington and Bragg in characteristic 3, some lifts over W_2(k) do not extend over W_3(k). This disproves a conjecture of Achinger and Zdanowicz.
ER -