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We prove a common slot lemma for symbols in top cohomology classes over semiglobal fields. Furthermore, we prove that period and index agree for general top cohomology classes over such fields. We discuss applications to quadratic forms and related open problems.

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Period-Index in Top Cohomology Over Semiglobal Fields

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Sarah Dijols,
  • Raman Parimala,
  • Sujatha Ramdorai,
  • Charlotte Ure

摘要

We prove a common slot lemma for symbols in top cohomology classes over semiglobal fields. Furthermore, we prove that period and index agree for general top cohomology classes over such fields. We discuss applications to quadratic forms and related open problems.