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<p>In this note, we connect the <i>n</i>-torsions of the Picard group of an elliptic surface to the <i>n</i>-divisibility of the class group of torsion fields for a given integer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We also connect the <i>n</i>-divisibility of the Selmer group to that of the class group of torsion fields.</p>

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Elliptic surfaces to class groups and Selmer groups

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Kalyan Banerjee,
  • Kalyan Chakraborty,
  • Azizul Hoque

摘要

In this note, we connect the n-torsions of the Picard group of an elliptic surface to the n-divisibility of the class group of torsion fields for a given integer \(n>1\) n > 1 . We also connect the n-divisibility of the Selmer group to that of the class group of torsion fields.