1. Splitting Brauer classes using the universal Albanese
- Author
-
Wei Ho and Max Lieblich
- Subjects
Abelian variety ,Class (set theory) ,Mathematics - Number Theory ,14F22, 14K30, 16K50 ,Modulo ,Field (mathematics) ,Mathematics - Rings and Algebras ,Combinatorics ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Albanese variety ,Rings and Algebras (math.RA) ,Genus (mathematics) ,Torsor ,FOS: Mathematics ,Number Theory (math.NT) ,Algebraic Geometry (math.AG) ,Mathematics - 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., Comment: 11 pages, references and acknowledgments updated, comments welcome at any time
- Published
- 2021
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