Splitting Brauer classes using the universal Albanese

2018/05/31 by Ho, Wei, Lieblich, Max · 2 citations
#14F22 #14K30 #16K50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1805.12566

Abstract

We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the class also splits the class, and there exist many such curves splitting the class. We show that this can be false when the index is congruent to 2 modulo 4, but adding a single genus 1 factor to the Albanese suffices to split the class.

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• Splitting Brauer classes by genus one curves over number fields
• Brauer classes not split by genus one curves

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