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Fine Selmer Groups and Isogeny Invariance
We investigate fine Selmer groups for elliptic curves and for Galois
representations over a number field. More specifically, we discuss Conjecture
A, which states that the fine Selmer group of an elliptic curve over the
cyclotomic extension is a finitely generated -module. The
relationship between this conjecture and Iwasawa's classical conjecture
is clarified. We also present some partial results towards the question whether
Conjecture A is invariant under isogenies.Comment: 20 page