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 of its period.

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Publication Details

Journal
Mathematische Annalen
Published
2025-04-26
DOI
https://doi.org/10.1007/s00208-025-03161-2
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

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

Daniel Huybrechts, Dominique Mattei
Mathematische Annalen
Finite Group Theory Research
article

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

Daniel Huybrechts, Dominique Mattei
article en

Abstract

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.

Mathematische AnnalenVol. 392(2)
University of Bonn (DE)
Eidgenössische Technische Hochschule Zürich, Rheinische Friedrich-Wilhelms-Universität Bonn, HORIZON EUROPE European Research Council
Openalex Percentile: Top 87%
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
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Splitting unramified Brauer classes by abelian torsors and the period-index problem — Daniel Huybrechts, Dominique Mattei · Mathematische Annalen (2025) | TGRS Research Map | TGRS