Splitting Brauer classes using the universal Albanese

  • Wei Ho

    University of Michigan, Ann Arbor, USA
  • Max Lieblich

    University of Washington, Seattle, USA
Splitting Brauer classes using the universal Albanese cover

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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.

Cite this article

Wei Ho, Max Lieblich, Splitting Brauer classes using the universal Albanese. Enseign. Math. 67 (2021), no. 1/2, pp. 209–224

DOI 10.4171/LEM/1009