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<p>We show that there exist Brauer classes over a field <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>F</mi> </math></EquationSource> <EquationSource Format="TEX">$F$</EquationSource> </InlineEquation> which are not split by any genus one curve over <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>F</mi> </math></EquationSource> <EquationSource Format="TEX">$F$</EquationSource> </InlineEquation>. This answers a question of Clark and Saltman.</p>

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Brauer classes not split by genus one curves

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Zinovy Reichstein,
  • Federico Scavia

摘要

We show that there exist Brauer classes over a field F $F$ which are not split by any genus one curve over F $F$ . This answers a question of Clark and Saltman.