On the structure of Selmer groups over -adic Lie extensions

By Y. Ochi, O. Venjakob. 2002

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MODULES OVER IWASAWA ALGEBRAS (2001, background): “s are known, see [CH], where X(E/Fcyc) has positive µ-invariant, and for these examples X(E/F∞) cannot be ﬁnitely generated over Λ(H)). A second basic result about X(E/F∞) is due to Ochi and Venjakob [OV]. Proposition 7.3. Assume that hypothesis (i), (ii) and (iii) of Prop. 7.2 are valid. If X(E/F∞)”
On the structure theory of the Iwasawa algebra of a p-adic Lie group (2001, methodology): “For a detailed discussion of its arithmetic applications we refer the reader to [ 29 ] and a forthcoming paper [35].”
On the two-variable Iwasawa main conjecture (2006, background): “Note that Ext1 R(W � /W, R) is zero since W � /W is pseudo-null (see [ OV , Proposition 3.4] for example).”
Computations in non‐commutative Iwasawa theory (2005, unknown): “4) μGK (X(E/F∞)) = μΓK (X(E/K )), where GK is the pro-p group given by GK = Gal(F∞/K), and μGK (M) denotes the μ-invariant of any finitely generated torsion Λ(GK)-module M as defined in [28, 35], and similarly μΓK (R) denotes the μ-invariant of a finitely generated torsion Λ(ΓK)module R.”
Fine Selmer groups of elliptic curves over p-adic Lie extensions (2005, background): “When E does not have complex multiplication, the finite generation of X(E/F∞) over �(H ) is proven in [2], and the fact that the �(H ) -torsion submodule is zero is proven in [ 21 ].”