Iwasawa theory of fine Selmer groups associated to Drinfeld modules

Let be a prime power and be the rational function field over , the field with elements. Let be a Drinfeld module over and be a nonzero prime ideal of . Over the constant ‐extension of , we introduce the fine Selmer group associated to the ‐primary torsion of . We show that it is a cofinitely generated module over . This proves an analogue of Iwasawa's conjecture in this setting, and provides context for the further study of the objects that have been introduced in this article.