Period-index bounds for arithmetic threefolds
Algebraic Geometry
2020-08-03 v3 Rings and Algebras
Abstract
The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a -adic field predicts that the index divides the cube of the period. Using Gabber's theory of prime-to- alterations and the deformation theory of twisted sheaves, we prove that the index divides the fourth power of the period for every Brauer class whose period is prime to , giving the first uniform period-index bounds over such fields.
Keywords
Cite
@article{arxiv.1704.05489,
title = {Period-index bounds for arithmetic threefolds},
author = {Benjamin Antieau and Asher Auel and Colin Ingalls and Daniel Krashen and Max Lieblich},
journal= {arXiv preprint arXiv:1704.05489},
year = {2020}
}
Comments
Final version, to appear in Inventiones