Title: Fine Selmer Groups and Isogeny Invariance,
Abstract: 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 $\mathbb{Z}_p$-module. The
relationship between this conjecture and Iwasawa's classical $\mu=0$ conjecture
is clarified. We also present some partial results towards the question whether
Conjecture A is invariant under isogenies.