Non-liftable varieties via etale cohomology rings

Runjie Hu; Siqing Zhang

Non-liftable varieties via etale cohomology rings

Algebraic Geometry 2026-07-20 v1

Authors: Runjie Hu , Siqing Zhang

Abstract

We construct a smooth projective variety in positive characteristic whose $\mathbb{Q}_{\ell}$ -coefficient etale cohomology ring is not the scalar extension of any graded $\mathbb{Q}$ -algebra, providing an example of a new type of obstruction to characteristic zero liftability.

Keywords

non-liftable variety étale cohomology ring positive characteristic obstruction smooth projective variety

Cite

@article{arxiv.2607.18588,
  title  = {Non-liftable varieties via etale cohomology rings},
  author = {Runjie Hu and Siqing Zhang},
  journal= {arXiv preprint arXiv:2607.18588},
  year   = {2026}
}