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<p>In this note, we define the notion of Tate–Shafarevich group and Selmer group of the Chow group of zero cycles of degree zero of an abelian variety defined over a global function field and prove that the Selmer group is finite.</p>

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Finiteness of Selmer groups associated to degree zero cycles on an abelian variety over a global function field

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Kalyan Banerjee,
  • Kalyan Chakraborty

摘要

In this note, we define the notion of Tate–Shafarevich group and Selmer group of the Chow group of zero cycles of degree zero of an abelian variety defined over a global function field and prove that the Selmer group is finite.