Splitting unramified Brauer classes by abelian torsors and the period-index problem

We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power o...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Huybrechts, Daniel, Mattei, Dominique
Format: Article
Language:English
Online Access:Get full text
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Summary:We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power of its period.
ISSN:2331-8422