Brauer classes not split by genus one curves

2025/08/10 by Reichstein, Zinovy, Scavia, Federico · 1 citation
#14H52 #14K05 (Secondary) #16K50 (Primary) 12G05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.07447

Abstract

We show that there exist Brauer classes over a field F which are not split by any genus one curve over F. This answers a question of Clark and Saltman.

Citations

• Elliptic curves and their principal homogeneous spaces: splitting Severi--Brauer varieties
• Splitting unramified Brauer classes by abelian torsors and the period-index problem
• The Period and Index of a Generic Geometrically Elliptic Normal Curve
• Explicit descent on elliptic curves and splitting Brauer classes
• Genus 1 Curves in Severi--Brauer Surfaces
• Splitting Brauer classes using the universal Albanese
• Genus one curves and Brauer-Severi varieties

Cited by

• Splitting Brauer classes by genus one curves over number fields

Related

• Genus one curves and Brauer-Severi varieties
• Splitting Brauer classes using the universal Albanese
• Splitting Brauer classes by genus one curves over number fields
• Some properties of a Brauer class
• Explicit descent on elliptic curves and splitting Brauer classes