English

Moret-Bailly families and non-liftable schemes

Algebraic Geometry 2021-07-01 v3

Abstract

Generalizing the Moret-Bailly pencil of supersingular abelian surfaces to higher dimensions, we construct for each field of characteristic p>0 a smooth projective variety with trivial dualizing sheaf that does not formally lift to characteristic zero. Our approach heavily relies on local unipotent group schemes, the Beauville--Bogomolov Decomposition for K\"ahler manifolds with c1=0c_1=0, and equivariant deformation theory

Keywords

Cite

@article{arxiv.2006.16775,
  title  = {Moret-Bailly families and non-liftable schemes},
  author = {Damian Roessler and Stefan Schröer},
  journal= {arXiv preprint arXiv:2006.16775},
  year   = {2021}
}

Comments

31 pages, Theorem 5.1 extended to the case that \omega_Y is anti-nef, results on non-existence of formal liftings corrected by adding assumptions, Section 9 on non-existence of liftings to rings of Witt vectors added