English

The period-index conjecture is false

Algebraic Geometry 2026-08-04 v1

Abstract

For any uncountable algebraically closed field kk of characteristic 00 and any d3d \geq 3, we construct a variety over kk of dimension dd with a Brauer class which violates the period-index conjecture for Hodge-theoretic reasons. When d=3d = 3, our construction works even without the assumption that kk is uncountable; in particular, the period-index conjecture fails over Q\overline{\mathbf{Q}}.

Cite

@article{arxiv.2608.03684,
  title  = {The period-index conjecture is false},
  author = {Alexander Perry},
  journal= {arXiv preprint arXiv:2608.03684},
  year   = {2026}
}

Comments

17 pages