Proves that dual fine Selmer groups are finitely generated, indicating possible connections to conjectures in number theory.
We prove that the dual fine Selmer group of an abelian variety over the unramified Zₚ-extension of a function field is finitely generated over Zₚ. This is a function field version of a conjecture of Coates--Sujatha. We further prove that the fine Selmer group is finite (respectively zero) if the separable p-primary torsion of the abelian variety is finite (respectively zero).
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Ghosh et al. (2024) studied this question.
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