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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月26日

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  • Daniel Huybrechts,
  • Dominique Mattei

摘要

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.