The period-index conjecture is false
Algebraic Geometry
2026-08-04 v1
Abstract
For any uncountable algebraically closed field of characteristic and any , we construct a variety over of dimension with a Brauer class which violates the period-index conjecture for Hodge-theoretic reasons. When , our construction works even without the assumption that is uncountable; in particular, the period-index conjecture fails over .
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